Training experience 12.22

Before doing a bit vjudge number theory module, do some summary
1, prime number sieve, sieve for various multiplicative function
2, $s(p^{n})=1+p+p^2+...+p^n$ , using geometric series summation, too $s(p^n)=\frac{(p^{n+1}-1)}{p-1}$
3, looking for cycles, cycle found $T$ then you can on $T$ modulo
4, $gcd(a^{m-1},a^{n-1}) = a^{gcd(m,n)}-1$ promotion:
if $gcd(a,b)=1$
Ze $gcd(a^m-b^m,a^n-b^n) = a^{gcd(m,n)}-b^{gcd(m,n)}$