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A+b+c divides a²+b²+c²

Source: QEDMO 2005

November 8, 2005
modular arithmeticnumber theory proposednumber theory

Problem Statement

Let a,b,ca,b,c be positive integers such that a2+b2+c2a^2+b^2+c^2 is divisble by a+b+ca+b+c. Prove that at least two of the numbers a3,b3,c3a^3,b^3,c^3 leave the same remainder by division through a+b+ca+b+c.
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