Problems & Puzzles:
Collection 20th
Coll.20th016.
"Good residues" r mod p
On May 17, 2018,
Jaroslaw Wroblewski,
wrote:
Let p be a prime number. It is a straightforward consequence of Fermat's
little theorem that for any integer r:
(r+1)^p=r^p+1 (mod p).
We will call r a "good residue" mod p if
0<=r<p and the following
stronger condition holds:(r+1)^p=r^p+1
(mod p^2).
Q. Prove that
for any prime p, the number of good residues mod p is NOT
divisible
by 3.
