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moving between lattice point if distance=p

Source: Mongolian MO 2002 Grade 10 P2

April 9, 2021
geometrynumber theory

Problem Statement

For a natural number pp, one can move between two points with integer coordinates if the distance between them equals pp. Find all prime numbers pp for which it is possible to reach the point (2002,38)(2002,38) starting from the origin (0,0)(0,0).
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