Problem #PRU-76543

Problems Algebra and arithmetic Number theory. Divisibility Division with remainders. Arithmetic of remainders Division with remainder Methods Pigeonhole principle Pigeonhole principle (other)

12–15 3.0

Problem

Prove that, for any integer $n$ , among the numbers $n, n + 1, n + 2, \dots, n + 9$ there is at least one number that is mutually prime with the other nine numbers.

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