MathDB
2013 Team #9: S_m, the property mansion

Source:

March 1, 2013
number theoryrelatively prime

Problem Statement

Let mm be an odd positive integer greater than 11. Let SmS_m be the set of all non-negative integers less than mm which are of the form x+yx+y, where xy−1xy-1 is divisible by mm. Let f(m)f(m) be the number of elements of SmS_m.
(a) Prove that f(mn)=f(m)f(n)f(mn)=f(m)f(n) if mm, nn are relatively prime odd integers greater than 11. (b) Find a closed form for f(pk)f(p^k), where k>0k>0 is an integer and pp is an odd prime.
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