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Number of lattice points inside triangle

Source: Russian TST 2021, Day 8 P2

March 21, 2023
number theorylattice points

Problem Statement

The natural numbers tt{} and qq{} are given. For an integer ss{}, we denote by f(s)f(s) the number of lattice points lying in the triangle with vertices (0;−t/q),(0;t/q)(0;-t/q), (0; t/q) and (t;ts/q)(t; ts/q). Suppose that qq{} divides rs−1rs-1{}. Prove that f(r)=f(s)f(r) = f(s).
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