Infinitely many lattice points
Source: Latvian TST for Baltic Way 2020 P14
October 18, 2020
Number theory problemslattice pointsnumber theory
Problem Statement
Prove that there are infinitely many different triangles in coordinate plane satisfying:
1) their vertices are lattice points
2) their side lengths are consecutive integers
Remark: Triangles that can be obtained by rotation or translation or shifting the coordinate system are considered as equal triangles