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The principal thrust of this investigation is to provide families of quadratic polynomials fDkðXÞ 1⁄4 f 2 k X 2 þ 2ekX þ CgkAN; where ek f 2 k C 1⁄4 n (for any given nonzero integer n) satisfying the property that for any XAN; the period length ck 1⁄4 cð ffiffiffiffiffiffiffiffiffiffiffiffiffiffi DkðXÞ p Þ of the simple continued fraction expansion of… (More)
The purpose of this article is to provide criteria for the solvability of the Diophantine equation a2X2− bY 2 = c in terms of the simple continued fraction expansion of √ a2b, and to explore criteria for the solvability of AX2 − BY 2 = C for given A, B, C ∈ N in the general case. This continues work in –.
Mathematics is the queen of sciences and number theory is the queen of mathematics. But why is it computer science? It turns out to be critical for cryptography!