Interesting inequality
by sqing, May 31, 2025, 2:54 AM
Let 
Prove that
Prove that
find question
by mathematical-forest, May 29, 2025, 10:19 AM
Are there any contest questions that seem simple but are actually difficult? 
Tough inequality
by TUAN2k8, May 28, 2025, 2:03 AM
Let 
be an even integer and let 
be real numbers satisfying 
.
Prove that
be an even integer and let 
be real numbers satisfying 
.Prove that
This post has been edited 1 time. Last edited by TUAN2k8, 5 hours ago
Reason: .
Reason: .
Own made functional equation
by Primeniyazidayi, May 26, 2025, 7:39 PM
Find all functions 
such that 
for all 
such that 
for all 
Reflected point lies on radical axis
by Mahdi_Mashayekhi, Apr 19, 2025, 11:01 AM
Given is an acute and scalene triangle 
with circumcenter 
. 
and 
intersect the altitude from 
to 
at points 
and 
respectively. 
is the circumcenter of triangle 
and 
is the reflection of over . 
is the second intersection of circumcircles of triangles 
and 
. Show that 
are collinear.
with circumcenter 
. 
and 
intersect the altitude from 
to 
at points 
and 
respectively. 
is the circumcenter of triangle 
and 
is the reflection of over . 
is the second intersection of circumcircles of triangles 
and 
. Show that 
are collinear.This post has been edited 1 time. Last edited by Mahdi_Mashayekhi, Apr 19, 2025, 11:25 AM
Central sequences
by EeEeRUT, Apr 16, 2025, 1:37 AM
An infinite increasing sequence 
of positive integers is called central if for every positive integer 
, the arithmetic mean of the first 
terms of the sequence is equal to .
Show that there exists an infinite sequence
of positive integers such that for every central sequence 
there are infinitely many positive integers with 
.
of positive integers is called central if for every positive integer 
, the arithmetic mean of the first 
terms of the sequence is equal to .Show that there exists an infinite sequence
of positive integers such that for every central sequence 
there are infinitely many positive integers with 
.This post has been edited 3 times. Last edited by EeEeRUT, May 11, 2025, 11:47 AM
Guess period of function
by a1267ab, Dec 14, 2024, 11:16 PM
Let be a positive integer. Ana and Banana play a game. Banana thinks of a function 
and a prime number 
. He tells Ana that 
is nonconstant, 
, and 
for all integers 
. Ana's goal is to determine the value of . She writes down integers 
. After seeing this list, Banana writes down 
in order. Ana wins if she can determine the value of from this information. Find the smallest value of for which Ana has a winning strategy.
Anthony Wang
be a positive integer. Ana and Banana play a game. Banana thinks of a function 
and a prime number 
. He tells Ana that 
is nonconstant, 
, and 
for all integers 
. Ana's goal is to determine the value of . She writes down integers 
. After seeing this list, Banana writes down 
in order. Ana wins if she can determine the value of from this information. Find the smallest value of for which Ana has a winning strategy.Anthony Wang
Number Theory
by fasttrust_12-mn, Aug 15, 2024, 11:19 PM
Find all positive intgers 
and 
such that 
and 
is a prime number
and 
such that 
and 
is a prime numberThis post has been edited 1 time. Last edited by fasttrust_12-mn, Aug 15, 2024, 11:19 PM
and 
Find the value of 
Inequality with abc=1
by tenplusten, May 15, 2016, 7:48 AM
Let 
be positive reals such that 
.Prove the inequality 
This post has been edited 1 time. Last edited by tenplusten, May 15, 2016, 7:49 AM
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