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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

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0 replies
jlacosta
Mar 2, 2025
0 replies
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k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
J
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k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
J
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Exquality
giangtruong13   2
N 18 minutes ago by lbh_qys
Let $x,y,z>0$ satisfy that: $(xz)^2+(yz)^2+1 \leq 3z$. Find the minimum value: $$P=\frac{1}{(x+1)^2}+\frac{8}{(y+3)^2}+\frac{4z^2}{(1+2z)^2}$$
2 replies
giangtruong13
an hour ago
lbh_qys
18 minutes ago
J
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Problem 2830
sqing   0
25 minutes ago
Source: SXTB (2)2025
Let $ a,b>0 $ and $ \frac{1}{a^2+1}+ \frac{1}{b^2+1}=t $ $(1<t<2). $ Find the value range of $ a+b. $
h
0 replies
1 viewing
sqing
25 minutes ago
0 replies
J
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IMO PSC said it's not novel, but it's still very pretty
mshtand1   1
N 38 minutes ago by Rushery_10
Source: Ukrainian Mathematical Olympiad 2025. Day 1, Problem 10.3
It is known that some \(d\) distinct divisors of a positive integer number \(n\) form an arithmetic progression. Prove that the number \(n\) has at least \(2d - 2\) divisors.

Proposed by Anton Trygub
1 reply
mshtand1
Mar 13, 2025
Rushery_10
38 minutes ago
J
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geometry party
pnf   1
N an hour ago by Tsikaloudakis
https://artofproblemsolving.com/community/c4260013_geometry_party
1 reply
pnf
Yesterday at 1:51 PM
Tsikaloudakis
an hour ago
J
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chat gpt
fuv870   31
N an hour ago by Quantum-Phantom
The chat gpt alreadly knows how to solve the problem of IMO USAMO and AMC?
31 replies
fuv870
Yesterday at 9:51 PM
Quantum-Phantom
an hour ago
J
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Find the value
sqing   3
N an hour ago by sqing
Source: Own
Let $a,b,c$ be distinct real numbers such that $ \frac{a^2}{(a-b)^2}+ \frac{b^2}{(b-c)^2}+ \frac{c^2}{(c-a)^2} =1. $ Find the value of $\frac{a}{a-b}+ \frac{b}{b-c}+ \frac{c}{c-a}.$
Let $a,b,c$ be distinct real numbers such that $\frac{a^2}{(b-c)^2}+ \frac{b^2}{(c-a)^2}+ \frac{c^2}{(a-b)^2}=2. $ Find the value of $\frac{a}{b-c}+ \frac{b}{c-a}+ \frac{c}{a-b}.$
Let $a,b,c$ be distinct real numbers such that $\frac{(a+b)^2}{(a-b)^2}+ \frac{(b+c)^2}{(b-c)^2}+ \frac{(c+a)^2}{(c-a)^2}=2. $ Find the value of $\frac{a+b}{a-b}+\frac{b+c}{b-c}+ \frac{c+a}{c-a}.$
3 replies
sqing
4 hours ago
sqing
an hour ago
J
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Kaprekar Number
CSJL   4
N an hour ago by Korean_fish_Kaohsiung
Source: 2025 Taiwan TST Round 1 Independent Study 2-N
Let $k$ be a positive integer. A positive integer $n$ is called a $k$-good number if it satisfies
the following two conditions:

1. $n$ has exactly $2k$ digits in decimal representation (it cannot have leading zeros).

2. If the first $k$ digits and the last $k$ digits of $n$ are considered as two separate $k$-digit
numbers (which may have leading zeros), the square of their sum is equal to $n$.

For example, $2025$ is a $2$-good number because
\[(20 + 25)^2 = 2025.\]Find all $3$-good numbers.
4 replies
CSJL
Mar 6, 2025
Korean_fish_Kaohsiung
an hour ago
J
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Functional Inequality Implies Uniform Sign
peace09   30
N 2 hours ago by Nari_Tom
Source: 2023 ISL A2
Let $\mathbb{R}$ be the set of real numbers. Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a function such that \[f(x+y)f(x-y)\geqslant f(x)^2-f(y)^2\]for every $x,y\in\mathbb{R}$. Assume that the inequality is strict for some $x_0,y_0\in\mathbb{R}$.

Prove that either $f(x)\geqslant 0$ for every $x\in\mathbb{R}$ or $f(x)\leqslant 0$ for every $x\in\mathbb{R}$.
30 replies
peace09
Jul 17, 2024
Nari_Tom
2 hours ago
J
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orthogonality
karimeow   0
2 hours ago
Given a cyclic quadrilateral ABCD inscribed in the circle (O). Let E and F be the intersections of AD with BC and AC with BD, respectively. Prove that the circle with diameter EF is orthogonal to (O).
0 replies
karimeow
2 hours ago
0 replies
J
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Problem 4
teps   73
N 2 hours ago by Nari_Tom
Find all functions $f:\mathbb Z\rightarrow \mathbb Z$ such that, for all integers $a,b,c$ that satisfy $a+b+c=0$, the following equality holds:
\[f(a)^2+f(b)^2+f(c)^2=2f(a)f(b)+2f(b)f(c)+2f(c)f(a).\]
(Here $\mathbb{Z}$ denotes the set of integers.)

Proposed by Liam Baker, South Africa
73 replies
teps
Jul 11, 2012
Nari_Tom
2 hours ago
J
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Did this get posted yet
pog   27
N 2 hours ago by ohiorizzler1434
Source: 2024 AMC 8 #1
What is the ones digit of \[222{,}222-22{,}222-2{,}222-222-22-2?\]
$\textbf{(A) }0\qquad\textbf{(B) }2\qquad\textbf{(C) }4\qquad\textbf{(D) }6\qquad\textbf{(E) }8$
27 replies
pog
Oct 11, 2024
ohiorizzler1434
2 hours ago
J
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AIME score for college apps
Happyllamaalways   80
N 3 hours ago by aliz
What good colleges do I have a chance of getting into with an 11 on AIME? (Any chances for Princeton)

Also idk if this has weight but I had the highest AIME score in my school.
80 replies
1 viewing
Happyllamaalways
Mar 13, 2025
aliz
3 hours ago
J
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Easy Combinatorics
JetFire008   2
N 4 hours ago by MathRook7817
Source: AMC 12 2001
How many positive integers not exceeding $2001$ are multiples of $3$ or $4$ but not $5$?
2 replies
JetFire008
Yesterday at 4:32 PM
MathRook7817
4 hours ago
J
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AHSME Challenge
Silverfalcon   5
N 4 hours ago by Magnetoninja
Source: 0
For each positive integer $n$, let
\[a_n = \frac {(n + 9)!}{(n - 1)!}.\]
Let $k$ denote the smallest positive integer for which the rightmost nonzero digit of $a_k$ is odd. The rightmost nonzero digit of $a_k$ is

$ \textbf{(A)}\ 1\qquad \textbf{(B)}\ 3\qquad \textbf{(C)}\ 5\qquad \textbf{(D)}\ 7\qquad \textbf{(E)}\ 9$
5 replies
Silverfalcon
Jan 2, 2005
Magnetoninja
4 hours ago
J
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J
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Did this get posted yet
pog   27
N 2 hours ago by ohiorizzler1434
Source: 2024 AMC 8 #1
What is the ones digit of \[222{,}222-22{,}222-2{,}222-222-22-2?\]
$\textbf{(A) }0\qquad\textbf{(B) }2\qquad\textbf{(C) }4\qquad\textbf{(D) }6\qquad\textbf{(E) }8$
27 replies
pog
Oct 11, 2024
ohiorizzler1434
2 hours ago
J
Did this get posted yet
G H J
Reveal topic tags
2024 AMC 8
AMC
AMC 8
turning into flamewar
L
G H BBookmark kLocked kLocked NReply
Source: 2024 AMC 8 #1
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pog
4917 posts
pog
#1 h  Oct 11, 2024, 2:09 PM • 2 Y
Y by centslordm, Yrock
What is the ones digit of \[222{,}222-22{,}222-2{,}222-222-22-2?\]
$\textbf{(A) }0\qquad\textbf{(B) }2\qquad\textbf{(C) }4\qquad\textbf{(D) }6\qquad\textbf{(E) }8$
Z K Y
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fruitmonster97
2389 posts
fruitmonster97
#2 h  Oct 11, 2024, 2:17 PM • 1 Y
Y by megarnie
I don't believe this has been posted yet, somehow? That's funny.

Anyways this should be $2-2-2-2-2-2\equiv-8\equiv\boxed{2}\pmod{10},$ answer choice $\textbf{(B)}.$
Z K Y
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ethanzhang1001
1070 posts
ethanzhang1001
#3 h  Oct 11, 2024, 2:24 PM
Y by
wait yeah thats true no one posted it :rotfl:

In-competition I just set it as $22 - 2 - 2 - 2 - 2 - 2=22-10\implies \boxed{\textbf{(B) }2}$.
This post has been edited 1 time. Last edited by ethanzhang1001, Oct 11, 2024, 2:24 PM
Z K Y
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andliu766
102 posts
andliu766
#4 h  Oct 11, 2024, 11:48 PM
Y by
$222,222 - 22,222 - 2,222 - 222 -22 -2 \equiv 2 - 2 - 2 - 2 - 2 - 2 \equiv \boxed{2} \pmod{n}$.
very simple ...
Z K Y
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SteadyLeopard38
21 posts
SteadyLeopard38
#5 h  Oct 12, 2024, 12:03 AM
Y by
the answer is B
Z K Y
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NoSignOfTheta
1681 posts
NoSignOfTheta
#6 h  Oct 12, 2024, 12:10 AM
Y by
$2 * 6 = 12, 12$ mod $10 = 2$
This post has been edited 1 time. Last edited by NoSignOfTheta, Oct 12, 2024, 12:10 AM
Z K Y
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Sidein98
344 posts
Sidein98
#7 h  Oct 12, 2024, 12:12 AM
Y by
10-2-2-2-2=2 b
Z K Y
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vincentwant
1235 posts
vincentwant
#8 h  Oct 12, 2024, 3:55 PM • 1 Y
Y by aidan0626
on the actual amc 8 i literally spent a whole minute doing $222222-22222-2222-222-22-2$ before realizing that it asked for the units digit :skull:
Z K Y
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andliu766
102 posts
andliu766
#9 h  Oct 13, 2024, 1:02 AM
Y by
vincentwant wrote:
on the actual amc 8 i literally spent a whole minute doing $222222-22222-2222-222-22-2$ before realizing that it asked for the units digit :skull:

ADMITS
You still perfect scored though...
Z K Y
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shilad11
785 posts
shilad11
#10 h  Oct 13, 2024, 1:11 AM
Y by
it has to always be 2
Z K Y
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vincentwant
1235 posts
vincentwant
#11 h  Oct 13, 2024, 1:47 AM
Y by
andliu766 wrote:
vincentwant wrote:
on the actual amc 8 i literally spent a whole minute doing $222222-22222-2222-222-22-2$ before realizing that it asked for the units digit :skull:

ADMITS
You still perfect scored though...

ADMITS NORZ
buh 39 min isnt that different from 40 min the p6 diagram not showing up was more of a timesink
Z K Y
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andliu766
102 posts
andliu766
#12 h  Oct 13, 2024, 3:58 AM
Y by
vincentwant wrote:
andliu766 wrote:
vincentwant wrote:
on the actual amc 8 i literally spent a whole minute doing $222222-22222-2222-222-22-2$ before realizing that it asked for the units digit :skull:

ADMITS
You still perfect scored though...

ADMITS NORZ
buh 39 min isnt that different from 40 min the p6 diagram not showing up was more of a timesink
ADMITS ORZ by prefect scoring with disadvantges
stop denying we all know you're orz vincent
Z K Y
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AshAuktober
917 posts
AshAuktober
#13 h  Oct 13, 2024, 4:16 AM
Y by
$$2-2-2-2-2-2 \equiv \boxed{2} \pmod{10}.$$
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gamer_doge543
363 posts
gamer_doge543
#14 h  Oct 31, 2024, 2:58 AM
Y by
The answer is B
Z K Y
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Yrock
1209 posts
Yrock
#15 h  Oct 31, 2024, 3:03 AM
Y by
$222222-22222-2222-222-22-2=2\cdot6-2\cdot5-2\cdot4-2\cdot3-2\cdot2-2\cdot1=2\cdot(-9)= -18 \equiv \boxed{2} (\mod 10)$


/j
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MC_ADe
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MC_ADe
#16 h  Oct 31, 2024, 11:44 AM
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got it wrong
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edoced
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edoced
#17 h  Dec 6, 2024, 5:55 AM
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222222 - 22222 - 2222 - 222 - 22 - 2 = 222222 - (22222 + 2222 + 222 + 22 + 2) -- the last digit of the sum of the last 5 numbers is 0, 2 - 0 = 2 so the answer is B
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JH_K2IMO
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JH_K2IMO
#18 h  Dec 10, 2024, 7:40 AM
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222,222-22,222-2,222-222-22-2
=200,000-2,444-24
=200,000-2,468
=197,532
The answer is (B) 2.
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Angrybanana
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Angrybanana
#19 h  Mar 12, 2025, 12:44 AM
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b
2-2-2-2-2-2=-8
-8+10=2
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xTimmyG
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xTimmyG
#21 h  Mar 12, 2025, 2:40 AM
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Because all the digits in the problem are 2, we can use the fundamental theorem of continous addition to conclude the answer is 2, or (B)
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derekli
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derekli
#22 h  Mar 12, 2025, 3:25 AM
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It's 2. Can we pls stop spamming these trivial problems
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NoSignOfTheta
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NoSignOfTheta
#23 h  Mar 12, 2025, 3:29 AM
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derekli wrote:
It's 2. Can we pls stop spamming these trivial problems

Yeah just stop. It's not trivial for some people and not everyone is as good at math as you are.
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derekli
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derekli
#24 h  Mar 12, 2025, 3:38 AM
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NoSignOfTheta wrote:
derekli wrote:
It's 2. Can we pls stop spamming these trivial problems

Yeah just stop. It's not trivial for some people and not everyone is as good at math as you are.

Ig you just need to know subtraction? seems pretty trivial to me (10th grade taking algebra 1 btw)
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aarush.rachak11
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aarush.rachak11
#25 h  Mar 12, 2025, 3:46 AM
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You're really good at math Derek Li!!
This post has been edited 1 time. Last edited by aarush.rachak11, Mar 12, 2025, 3:46 AM
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fake123
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fake123
#26 h  Mar 12, 2025, 5:43 AM
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NoSignOfTheta wrote:
derekli wrote:
It's 2. Can we pls stop spamming these trivial problems

Yeah just stop. It's not trivial for some people and not everyone is as good at math as you are.

brother
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santhoshn
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santhoshn
#27 h  Yesterday at 2:03 PM
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The answer is (B)2
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Jello0211
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Jello0211
#28 h  6 hours ago
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Answer is b) 2
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ohiorizzler1434
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ohiorizzler1434
#29 h  2 hours ago
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A fascinating application of the fundamental principles of modular arithmetic to simplify a calculation!
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