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On Cyclotomic Numbers of Order Sixteen
Published online by Cambridge University Press: 20 November 2018
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It has been shown by Dickson (1) that if (i, j)8 is the number of solutions of
(mod p),
then 64(i,j)8 is expressible for each i,j, as a linear combination with integer coefficients of p, x, y, a, and b where
,
and
a ≡ b ≡ 1 (mod 4),
while the sign of y and b depends on the choice of the primitive root g. There are actually four sets of such formulas depending on whether p is of the form 16n + 1 or 16n + 9 and whether 2 is a quartic residue or not.
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- Copyright © Canadian Mathematical Society 1954
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