Problem

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Tags: number theory proposed, number theory, Hi



g and n are natural numbers such that gcd(g2g,n)=1 and A={gi|iN} and B={x(n)|xA}(by x(n) we mean a number from the set {0,1,...,n1} which is congruent with x modulo n). if for 0ig1 ai=|[nig,n(i+1)g)B| prove that g1|g1i=0iai.( the symbol | | means the number of elements of the set)(1006 points) the exam time was 4 hours