.problem.
by Cobedangiu, Apr 4, 2025, 6:20 AM
Find the integer coefficients after expanding Newton's binomial:


This post has been edited 1 time. Last edited by Cobedangiu, Yesterday at 6:20 AM
Excalibur Identity
by jjsunpu, Apr 3, 2025, 3:27 PM
proof is below
This post has been edited 1 time. Last edited by jjsunpu, Yesterday at 12:19 AM
Reason: idk
Reason: idk
Probability
by Ecrin_eren, Apr 3, 2025, 11:21 AM
In a board, James randomly writes A , B or C in each cell. What is the probability that, for every row and every column, the number of A 's modulo 3 is equal to the number of B's modulo 3?
Congruence
by Ecrin_eren, Apr 3, 2025, 10:34 AM
Find the number of integer pairs (x, y) satisfying the congruence equation:
3y² + 3x²y + y³ ≡ 3x² (mod 41)
for 0 ≤ x, y < 41.
3y² + 3x²y + y³ ≡ 3x² (mod 41)
for 0 ≤ x, y < 41.
Inequalities
by sqing, Apr 1, 2025, 2:59 PM
Let
and
Prove that
Let
and
Prove that
Let
and
Prove that
Let
and
Prove that













Geo Mock #10
by Bluesoul, Apr 1, 2025, 7:06 AM
Consider acute
with
,
and area
. The circle
with diameter
meets
at
. Let the orthocenter of the triangle be
, connect
and extend to meet
at
such that
and
is the diameter of
. Draw the circumcircle
of
, chord
of
is tangent to
and it passes through
, compute
.






















L
Geo Mock #9
by Bluesoul, Apr 1, 2025, 7:05 AM
Consider
with
. The points
lie on
respectively, such that
. Extend
to meet the circumcircle of
at
respectively. Let the circumcircles of
meet at points
. Extend
to
at
, given
, find
.














![$[ABC]$](http://latex.artofproblemsolving.com/d/3/3/d33cc80fa8f093e155c5be46d2e5d9da3d7e1ef5.png)
L
Geo Mock #6
by Bluesoul, Apr 1, 2025, 7:04 AM
Consider triangle
with
, denote the incenter of the triangle as
. Extend
to meet the circumcircle of
at
, find the length of
.







L
Inequalities
by sqing, Mar 26, 2025, 3:07 AM
Let
and
. Prove that
Equality holds when 
Equality holds when 
Equality holds when 








"Where wisdom and valor fail, all that remains is faith. . . And it can overcome all." -Toa Mata Tahu
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