MathDB

Bulgaria 6

Source: BMO Problem 6

May 15, 2005

algebrapolynomialsymmetrymodular arithmeticnumber theory proposednumber theory

Problem Statement

Let

a,b

and

c

be positive integers such that

ab

divides

c(c^{2}-c+1)

and

a+b

is divisible by

c^{2}+1

. Prove that the sets

\{a,b\}

and

\{c,c^{2}-c+1\}

coincide.