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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Wednesday at 3:18 PM
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

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[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
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[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Wednesday at 3:18 PM
0 replies
J
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One of a,b,c,d is not greater than -1
WakeUp   5
N 26 minutes ago by Nari_Tom
Source: Baltic Way 2002
Let $a,b,c,d$ be real numbers such that
\[a+b+c+d=-2\]
\[ab+ac+ad+bc+bd+cd=0\]
Prove that at least one of the numbers $a,b,c,d$ is not greater than $-1$.
5 replies
WakeUp
Nov 13, 2010
Nari_Tom
26 minutes ago
J
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Product of first m primes
joybangla   4
N 34 minutes ago by Congruence
Source: European Mathematical Cup 2013, Junior Division, P1
For $m\in \mathbb{N}$ define $m?$ be the product of first $m$ primes. Determine if there exists positive integers $m,n$ with the following property :
\[ m?=n(n+1)(n+2)(n+3) \]

Proposed by Matko Ljulj
4 replies
joybangla
Jul 3, 2014
Congruence
34 minutes ago
J
H
a really nice polynomial problem
Etemadi   8
N an hour ago by amirhsz
Source: Iranian TST 2018, third exam day 1, problem 3
$n>1$ and distinct positive integers $a_1,a_2,\ldots,a_{n+1}$ are  given. Does there exist a polynomial $p(x)\in\Bbb{Z}[x]$ of degree  $\le n$ that satisfies the following conditions?
a. $\forall_{1\le i < j\le n+1}: \gcd(p(a_i),p(a_j))>1 $
b. $\forall_{1\le i < j < k\le n+1}: \gcd(p(a_i),p(a_j),p(a_k))=1 $

Proposed by Mojtaba Zare
8 replies
Etemadi
Apr 18, 2018
amirhsz
an hour ago
J
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Japanese NT
pomodor_ap   1
N an hour ago by Tkn
Source: Japan TST 2024 p6
Find all quadruples $(a, b, c, d)$ of positive integers such that
$$2^a3^b + 4^c5^d = 2^b3^a + 4^d5^c.$$
1 reply
pomodor_ap
Oct 5, 2024
Tkn
an hour ago
J
No more topics!
H
J
H
Position vectors of complex numbers
MetaphysicalWukong   5
N Mar 30, 2025 by Primeniyazidayi
Source: Dengyan Jin, Pinyao Cong
I cant even understand the question. Can someone help me?
5 replies
MetaphysicalWukong
Mar 30, 2025
Primeniyazidayi
Mar 30, 2025
J
Position vectors of complex numbers
G H J
Reveal topic tags
vector
complex numbers
algebra
L
G H BBookmark kLocked kLocked NReply
Source: Dengyan Jin, Pinyao Cong
The post below has been deleted. Click to close.
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MetaphysicalWukong
260 posts
MetaphysicalWukong
#1 h  Mar 30, 2025, 7:23 AM
Y by
I cant even understand the question. Can someone help me?
Attachments:
This post has been edited 2 times. Last edited by MetaphysicalWukong, Mar 30, 2025, 7:40 AM
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MetaphysicalWukong
260 posts
MetaphysicalWukong
#2 h  Mar 30, 2025, 7:24 AM
Y by
You may want to see this before:
Attachments:
This post has been edited 2 times. Last edited by MetaphysicalWukong, Mar 30, 2025, 7:30 AM
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Primeniyazidayi
37 posts
Primeniyazidayi
#3 h  Mar 30, 2025, 7:43 AM
Y by
I think you can take help from college forum.
Z K Y
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MetaphysicalWukong
260 posts
MetaphysicalWukong
#4 h  Mar 30, 2025, 7:44 AM
Y by
Primeniyazidayi wrote:
I think you can take help from college forum.
MetaphysicalWukong wrote:
I cant even understand the question. Can someone help me?

do u know anyone who may be able to help?
Z K Y
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MetaphysicalWukong
260 posts
MetaphysicalWukong
#6 h  Mar 30, 2025, 8:25 AM
Y by
bumping once more
Z K Y
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Primeniyazidayi
37 posts
Primeniyazidayi
#7 h  Mar 30, 2025, 8:51 AM
Y by
MetaphysicalWukong wrote:
Primeniyazidayi wrote:
I think you can take help from college forum.
MetaphysicalWukong wrote:
I cant even understand the question. Can someone help me?

do u know anyone who may be able to help?

See https://artofproblemsolving.com/community/c7_college_math
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