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n^6 + 5n^3 + 4n + 116 is the product of two or more consecutive numbers
Amir Hossein 2
N
an hour ago
by KTYC
Source: Bulgaria JBMO TST 2018, Day 1, Problem 3
Find all positive integers
such that the number
is the product of two or more consecutive numbers.


2 replies

IMO Shortlist 2009 - Problem G3
April 49
N
2 hours ago
by Ilikeminecraft
Let
be a triangle. The incircle of
touches the sides
and
at the points
and
, respectively. Let
be the point where the lines
and
meet, and let
and
be points such that the two quadrilaterals
and
are parallelogram.
Prove that
.
Proposed by Hossein Karke Abadi, Iran













Prove that

Proposed by Hossein Karke Abadi, Iran
49 replies
Four tangent lines concur on the circumcircle
v_Enhance 36
N
2 hours ago
by Ilikeminecraft
Source: USA TSTST 2018 Problem 3
Let
be an acute triangle with incenter
, circumcenter
, and circumcircle
. Let
be the midpoint of
. Ray
meets
at
. Denote by
and
the circumcircles of
and
, respectively. Line
meets
at
and
, while line
meets
at
and
. Assume that
lies inside
and
.
Consider the tangents to
at
and
and the tangents to
at
and
. Given that
, prove that these four lines are concurrent on
.
Evan Chen and Yannick Yao
























Consider the tangents to








Evan Chen and Yannick Yao
36 replies

Inequality
Amin12 8
N
3 hours ago
by A.H.H
Source: Iran 3rd round-2017-Algebra final exam-P3
Let
and
be positive real numbers. Prove that



8 replies
1 viewing
Every subset of size k has sum at most N/2
orl 50
N
4 hours ago
by de-Kirschbaum
Source: USAMO 2006, Problem 2, proposed by Dick Gibbs
For a given positive integer
find, in terms of
, the minimum value of
for which there is a set of
distinct positive integers that has sum greater than
but every subset of size
has sum at most







50 replies
Cute NT Problem
M11100111001Y1R 5
N
5 hours ago
by compoly2010
Source: Iran TST 2025 Test 4 Problem 1
A number
is called lucky if it has at least two distinct prime divisors and can be written in the form:
where
are distinct prime numbers that divide
. (Note: it is possible that
has other prime divisors not among
.) Prove that for every prime number
, there exists a lucky number
such that
.

![\[
n = p_1^{\alpha_1} + \cdots + p_k^{\alpha_k}
\]](http://latex.artofproblemsolving.com/7/4/4/744a5ccaeb9476ebd7d999c395762cb6e99a7a71.png)







5 replies
3 var inequality
SunnyEvan 13
N
5 hours ago
by Nguyenhuyen_AG
Let
,such that
Prove that :



13 replies
Polar Coordinates
pingpongmerrily 4
N
Today at 12:11 AM
by K124659
Convert the equation
into rectangular form.

4 replies
