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a,b,c,t

Source: Iranian National Olympiad (3rd Round) 2006

August 26, 2006
number theory proposednumber theory

Problem Statement

a,b,c,ta,b,c,t are antural numbers and k=ctk=c^{t} and n=ak−bkn=a^{k}-b^{k}. a) Prove that if kk has at least qq different prime divisors, then nn has at least qtqt different prime divisors. b)Prove that φ(n)\varphi(n) id divisible by 2t22^{\frac{t}{2}}
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