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the same prime factors

Source: Iranian third round number theory P4

September 6, 2015
number theoryfermat's little theorem

Problem Statement

a,b,c,d,k,la,b,c,d,k,l are positive integers such that for every natural number nn the set of prime factors of nk+an+c,nl+bn+dn^k+a^n+c,n^l+b^n+d are same. prove that k=l,a=b,c=dk=l,a=b,c=d.
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