Positive integers a, b, c are given. It is known that cb=ba, and the number b2−a−c+1 is a prime. Prove that a and c are double of a squares of positive integers.
Source: VII Caucasus Mathematical Olympiad
Tags: algebra, number theory, geometric sequence
Positive integers a, b, c are given. It is known that cb=ba, and the number b2−a−c+1 is a prime. Prove that a and c are double of a squares of positive integers.