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Polynomial solutions of binomial congruences
Published online by Cambridge University Press: 09 April 2009
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Polynomial solutions of a few binomial congruences have been known for a long time. For instance Legendre showed that the congruence 
has a solution 
this being the expansion of 
as far as the term of degree m — 3. [1] It seems that only restricted types, e.g. (1), have been investigated.
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- Copyright © Australian Mathematical Society 1960
References
For further polynomial and other explict solutions see Dickson, L. E., History of the Theory of Numbers, vol. 1, ch. VII.Google Scholar
[3]Uspensky, and Heaslet, , Elementary Number Theory, p. 103, ex. 1. Proved in Griffin H., Elementary Theory of Numbers, pp. 42–3.Google Scholar
[6]Cipolla, M. obtained (51) for a quadratic congruence in the following form. The solution of 
where (In (15) let on the right.) He later extended the exponent of x to any divisor of p — 1 (i.e. n=d and m = 1 in the notation used here), and found an equivalent of (50) for this case.Google Scholar
where 
(In (15) let 
on the right.) He later extended the exponent of x to any divisor of p — 1 (i.e. n=d and m = 1 in the notation used here), and found an equivalent of (50) for this case.Google Scholar
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