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Last Poster
a+b+c=2 ine
KhuongTrang 30
N
by KhuongTrang
Source: own
Problem. Given non-negative real numbers 
satisfying 
Prove that 
satisfying 
Prove that 
30 replies
2021 EGMO P1: {m, 2m+1, 3m} is fantabulous
anser 55
N
by NicoN9
Source: 2021 EGMO P1
The number 2021 is fantabulous. For any positive integer 
, if any element of the set 
is fantabulous, then all the elements are fantabulous. Does it follow that the number 
is fantabulous?
, if any element of the set 
is fantabulous, then all the elements are fantabulous. Does it follow that the number 
is fantabulous?
55 replies
Complicated FE
XAN4 0
Source: own
Find all solutions for the functional equation 
, in which 
: 
Note: the solution is actually quite obvious -
, but the proof is important.
Note 2: it is likely that the result can be generalized into a more advanced questions, potentially involving more bash.
, in which 
: 
Note: the solution is actually quite obvious -
, but the proof is important.Note 2: it is likely that the result can be generalized into a more advanced questions, potentially involving more bash.
0 replies
Feet of perpendiculars to diagonal in cyclic quadrilateral
jl_ 1
N
by navier3072
Source: Malaysia IMONST 2 2023 (Primary) P6
Suppose 
is a cyclic quadrilateral with 
. Let 
and 
be the feet of perpendiculars from 
and 
to 
respectively. Prove that 
.
is a cyclic quadrilateral with 
. Let 
and 
be the feet of perpendiculars from 
and 
to 
respectively. Prove that 
.
1 reply
IMO Shortlist 2014 N5
hajimbrak 58
N
by Jupiterballs
Find all triples 
consisting of a prime number 
and two positive integers 
and 
such that 
and 
are both powers of .
Proposed by Belgium
consisting of a prime number 
and two positive integers 
and 
such that 
and 
are both powers of .Proposed by Belgium
58 replies
Integer a_k such that b - a^n_k is divisible by k
orl 69
N
by ZZzzyy
Source: IMO Shortlist 2007, N2, Ukrainian TST 2008 Problem 10
Let 
be integers. Suppose that for each 
there exists an integer 
such that 
is divisible by 
. Prove that 
for some integer .
Author: Dan Brown, Canada
be integers. Suppose that for each 
there exists an integer 
such that 
is divisible by 
. Prove that 
for some integer .Author: Dan Brown, Canada
69 replies
interesting function equation (fe) in IR
skellyrah 1
N
by CrazyInMath
Source: mine
find all function F: IR->IR such that 
1 reply
Find maximum area of right triangle
jl_ 1
N
by navier3072
Source: Malaysia IMONST 2 2023 (Primary) P4
Given a right-angled triangle with hypothenuse 
, find the maximal area of the triangle.
, find the maximal area of the triangle.
1 reply
Erasing a and b and replacing them with a - b + 1
jl_ 1
N
by maromex
Source: Malaysia IMONST 2 2023 (Primary) P5
Ruby writes the numbers 
on the whiteboard. In each move, she selects two distinct numbers, 
and 
, erases them, and replaces them with 
. She repeats this process until only one number, , remains. What are all the possible values of ?
on the whiteboard. In each move, she selects two distinct numbers, 
and 
, erases them, and replaces them with 
. She repeats this process until only one number, , remains. What are all the possible values of ?
1 reply
Prove that sum of 1^3+...+n^3 is a square
jl_ 2
N
by NicoN9
Source: Malaysia IMONST 2 2023 (Primary) P1
Prove that for all positive integers 
, 
is a perfect square.
, 
is a perfect square.
2 replies
