Kvant Math Problem 1556

Working

kvantmathematicsolympiad

Verified: no
Verdicts: FAIL + FAIL
Solve time: 31m40s
Source on kvant.digital

Problem

Prove that there exist infinitely many triples of numbers $n-1$, $n$, $n+1$ such that:

  1. $n$ is representable as a sum of two squares of natural numbers, while $n-1$ and $n+1$ are not;
  2. each of these three numbers is representable as a sum of two squares of natural numbers.

V. A. Senderov

Moscow LIX Mathematical Olympiad 1996, Tournaments of the Towns (spring, 1996)

Working