Question

Find the
sum of
all the positive integers
and relativery prime
less than 2009 to 2009.​

Answer 1

Answer:

It’s true for all n>2. The reason is that if k∈{1,…,n−1} is relatively prime to n, so is n−k, so the integers that you’re adding can be combined into φ(n)2 pairs whose members sum to n. If n>2, n2 is never relatively prime to n, so you really do get pairs {k,n−k}.

See OEIS A023896 for some references.