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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).doi:10.1017/s0027763000000039 fatcat:6kfjcjci4jb6bjfuvdx6gulxu4