Problem #PRU-35344

Problems Algebra and arithmetic Number theory. Divisibility Division with remainders. Arithmetic of remainders Division with remainder Methods Pigeonhole principle Pigeonhole principle (other)
 13–14  3.0

Problem

Prove that if \(a, b, c\) are odd numbers, then at least one of the numbers \(ab-1\), \(bc-1\), \(ca-1\) is divisible by 4.