A Sum Connected with Quadratic Residues
L. Carlitz · Nagoya Mathematical Journal · 1956
Let p be a prime > 2 and m an arbitrary positive integer; define where (r/p) is the Legendre symbol. We consider the problem of finding the highest power of p dividing Sm. A little more generally, if we put where a is an arbitrary integer, we seek the highest power of p dividing Sm(a). Clearly Sm = Sm(0), and Sm(a) = Sm(b) when a ≡ b (mod p).