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a^3 + b^3 + c^3 is divisible by 6

Source: 2003 Bosnia & Herzegovina JBMO TST p3

May 27, 2020
dividesdivisiblenumber theory

Problem Statement

Let a,b,ca, b, c be integers such that the number a2+b2+c2a^2 +b^2 +c^2 is divisible by 66 and the number ab+bc+caab + bc + ca is divisible by 33. Prove that the number a3+b3+c3a^3 + b^3 + c^3 is divisible by 66.
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