Counting Solutions of Quadratic Congruences in Several Variables Revisited
نویسنده
چکیده
Let Nk(n, r,a) denote the number of incongruent solutions of the quadratic congruence a1x 2 1+ · · ·+akxk ≡ n (mod r), where a = (a1, . . . , ak) ∈ Zk, n ∈ Z, r ∈ N. We give short direct proofs for certain less known compact formulas on Nk(n, r,a), valid for r odd, which go back to the work of Minkowski, Bachmann and Cohen. We also deduce some other related identities and asymptotic formulas which do not seem to appear in the literature.
منابع مشابه
Quadratic Congruences
1 Quadratic Congruences to Prime Moduli . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Quadratic Congruences to Composite Moduli . . . . . . . . . . . . . . . . . . . . . 5 3 Some Sums of Legendre’s symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5 Solutions . . . . . . . . . . . . ...
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تاریخ انتشار 2014