Let denote the sum of the squares of the positive integers and prime to .
Prove that
I have trouble with separating the integers into classes, so that all integers such that are in the same class.
Thanks for the help.
Let denote the sum of the squares of the positive integers and prime to .
Prove that
I have trouble with separating the integers into classes, so that all integers such that are in the same class.
Thanks for the help.
Let , for each d|n, define x,n)=d\}" alt="N_d=\{x^2x,n)=d\}" />, then is a partion on N.
And for each , Since , By the definition of S(.), the sum of elements in is ,
Thus,the first equality of
is proved.
When d exhaust all the divisors of n, so do , Thus the second equality obviously hold.