be a convex quadrilateral and let 
be the point of intersection of 
and 
.
.
,
and 
meet at a common point.
be a positive integer and 
be a positive integer coprime to 
,
,
Find, in terms of 
,
such that 
is divisible by 
.
be an infinite sequence of positive integers, and let 
be a positive integer. Suppose that, for each 
,
is equal to the number of times 
appears in the list 
.
and 
is eventually periodic.
is eventually periodic if there exist positive integers 
and 
such that 
for all 
.
and a 
grid are given. We write down one integer to each of the square of the grid so that each of integer 
to 
are written exactly once in the grid, and no two adjacent square have sum prime.
Y by teomihai
Suppose you have an 
grid with 
rows and 
columns, and each square of the grid is filled with a non-negative integer. Let 
be the average of all the numbers in the grid. Prove that if 
the there exist two identical rows (meaning same numbers in the same order).
grid with 
rows and 
columns, and each square of the grid is filled with a non-negative integer. Let 
be the average of all the numbers in the grid. Prove that if 
the there exist two identical rows (meaning same numbers in the same order).This post has been edited 2 times. Last edited by Anto0110, Apr 5, 2025, 1:58 PM
Reason: 9
Reason: 9
