MathDB

Problem 2

Part of 2002 Mongolian Mathematical Olympiad

Problems(2)

moving between lattice point if distance=p

Source: Mongolian MO 2002 Grade 10 P2

4/9/2021
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).
geometrynumber theory
irreducible: (x^2+x)^(2^n)+1

Source: Mongolian MO 2002 Teachers P2

4/9/2021
Prove that for each nāˆˆNn\in\mathbb N the polynomial (x2+x)2n+1(x^2+x)^{2^n}+1 is irreducible over the polynomials with integer coefficients.
polynomialalgebrairreducibility