modular arithmeticalgebrapolynomialfunctionnumber theory proposednumber theory
Problem Statement
For any positive integer n and 0⩽i⩽n, denote Cni≡c(n,i)(mod2), where c(n,i)∈{0,1}. Define
f(n,q)=i=0∑nc(n,i)qi
where m,n,q are positive integers and q+1=2α for any α∈N. Prove that if f(m,q)∣f(n,q), then f(m,r)∣f(n,r) for any positive integer r.