Find all functions f:Z→Z such that the numbers
n,f(n),f(f(n)),…,fm−1(n)
are distinct modulo m for all integers n,m with m>1.
(Here fk is defined by f0(n)=n and fk+1(n)=f(fk(n)) for k≥0.) number theorynumber theory proposedfunctionresiduemodular arithmetic