for which the following statement is true: If positive integers 
and 
are such that 
is a multiple of 
and 
is a multiple of 
be an acute triangle with circumcenter 
.
,
on side 
.
passing through 
at point 
.
and 
the product of all 
.![$\sqrt[2024]{p(n)} \in \mathbb{Z}$](http://latex.artofproblemsolving.com/7/0/4/70442d4ec6ae8b7a3cf9717719e862bf3b5d4a28.png)
and is not a perfect power of another integer.
Y by
Let 
be a convex pentagon in the coordinate plane. Each of its vertices is an lattice point. The five diagonals of form a convex pentagon 
within . Prove that this smaller pentagon contains a lattice point on its edge or interior.
be a convex pentagon in the coordinate plane. Each of its vertices is an lattice point. The five diagonals of form a convex pentagon 
within . Prove that this smaller pentagon contains a lattice point on its edge or interior.This post has been edited 1 time. Last edited by parmenides51, Dec 16, 2022, 10:49 AM
