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Topic
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Rational sequences
tenniskidperson3 58
N
by meduh6849
Source: 2009 USAMO problem 6
Let 
be an infinite, nonconstant sequence of rational numbers, meaning it is not the case that 
Suppose that 
is also an infinite, nonconstant sequence of rational numbers with the property that 
is an integer for all 
and 
. Prove that there exists a rational number 
such that 
and 
are integers for all and .
be an infinite, nonconstant sequence of rational numbers, meaning it is not the case that 
Suppose that 
is also an infinite, nonconstant sequence of rational numbers with the property that 
is an integer for all 
and 
. Prove that there exists a rational number 
such that 
and 
are integers for all and .
58 replies
4th grader qual JMO
HCM2001 38
N
by blueprimes
i mean.. whattttt??? just found out about this.. is he on aops? (i'm sure he is) where are you orz lol..
https://www.mathschool.com/blog/results/celebrating-success-douglas-zhang-is-rsm-s-youngest-usajmo-qualifier
https://www.mathschool.com/blog/results/celebrating-success-douglas-zhang-is-rsm-s-youngest-usajmo-qualifier
38 replies
An FE. Who woulda thunk it?
nikenissan 120
N
by NerdyNashville
Source: 2021 USAJMO Problem 1
Let 
denote the set of positive integers. Find all functions 
such that for positive integers 
and 
![\[f(a^2 + b^2) = f(a)f(b) \text{ and } f(a^2) = f(a)^2.\]](//latex.artofproblemsolving.com/c/1/f/c1f8ffe04cfcc45b498f3931a4796d5c56dc04d0.png)
denote the set of positive integers. Find all functions 
such that for positive integers 
and 
![\[f(a^2 + b^2) = f(a)f(b) \text{ and } f(a^2) = f(a)^2.\]](http://latex.artofproblemsolving.com/c/1/f/c1f8ffe04cfcc45b498f3931a4796d5c56dc04d0.png)
120 replies
Zsigmondy's theorem
V0305 3
N
by CatCatHead
Is Zsigmondy's theorem allowed on the IMO, and is it allowed on the AMC series of proof competitions (e.g. USAJMO, USA TSTST)?
3 replies
Base 2n of n^k
KevinYang2.71 50
N
by ray66
Source: USAMO 2025/1, USAJMO 2025/2
Let 
and 
be positive integers. Prove that there exists a positive integer 
such that for every odd integer 
, the digits in the base-
representation of 
are all greater than .
and 
be positive integers. Prove that there exists a positive integer 
such that for every odd integer 
, the digits in the base-
representation of 
are all greater than .
50 replies
How Math WOOT Level 2 prepare you for olympiad contest
AMC10JA 0
I know how you do on Olympiad is based on your effort and your thinking skill, but I am just curious is WOOT level 2 is generally for practicing the beginner olympiad contest (like USAJMO or lower), or also good to learn for hard olympiad contest (like USAMO and IMO).
Please share your thought and experience. Thank you!
Please share your thought and experience. Thank you!
0 replies
Equilateral triangle $ABC$, $DEF$ has twice the area
v_Enhance 122
N
by lpieleanu
Source: JMO 2017 Problem 3, Titu, Luis, Cosmin
Let 
be an equilateral triangle, and point 
on its circumcircle. Let 
and 
intersect at 
, 
and 
intersect at 
, and 
and 
intersect at 
. Prove that the area of 
is twice the area of 
.
Proposed by Titu Andreescu, Luis Gonzales, Cosmin Pohoata
be an equilateral triangle, and point 
on its circumcircle. Let 
and 
intersect at 
, 
and 
intersect at 
, and 
and 
intersect at 
. Prove that the area of 
is twice the area of 
.Proposed by Titu Andreescu, Luis Gonzales, Cosmin Pohoata
122 replies
Perfect Square Dice
asp211 67
N
by A7456321
Source: 2019 AIME II #4
A standard six-sided fair die is rolled four times. The probability that the product of all four numbers rolled is a perfect square is 
, where 
and 
are relatively prime positive integers. Find 
.
, where 
and 
are relatively prime positive integers. Find 
.
67 replies
HCSSiM results
SurvivingInEnglish 75
N
by cowstalker
Anyone already got results for HCSSiM? Are there any point in sending additional work if I applied on March 19?
75 replies
Perfect squares: 2011 USAJMO #1
v_Enhance 227
N
by ray66
Find, with proof, all positive integers for which 
is a perfect square.
for which 
is a perfect square.
227 replies
