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Divisiblity by 5

Source: INMO 1998 Problem 3

October 7, 2005
number theory solvednumber theory

Problem Statement

Let p,q,r,sp , q, r , s be four integers such that ss is not divisible by 55. If there is an integer aa such that pa3+qa2+ra+spa^3 + qa^2+ ra +s is divisible be 5, prove that there is an integer bb such that sb3+rb2+qb+psb^3 + rb^2 + qb + p is also divisible by 5.
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