MathDB
sum of primitive root

Source: iran(third round 2003)

March 22, 2004
algebrapolynomialnumber theorynumber theory unsolved

Problem Statement

Let pp be an odd prime number. Let SS be the sum of all primitive roots modulo pp. Show that if p−1p-1 isn't squarefree (i. e., if there exist integers kk and mm with k>1k>1 and p−1=k2mp-1=k^2m), then S≡0mod  pS \equiv 0 \mod p.
If not, then what is SS congruent to mod  p\mod p ?
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