The Diophantine equation . II.

Cohn, J.H.E.

Displaying similar documents to “The Diophantine equation $x^{2} + 2^{k} = y^{n}$ . II.”

New theorems concerning the diophantine equation $x^{2} + D = 4 y^{q}$

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On the diophantine equation w+x+y = z, with wxyz = 2 3 5.

L. J. Alex, L. L. Foster (1995)

Revista Matemática de la Universidad Complutense de Madrid

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In this paper we complete the solution to the equation w+x+y = z, where w, x, y, and z are positive integers and wxyz has the form 2 3 5, with r, s, and t non negative integers. Here we consider the case 1 < w ≤ x ≤ y, the remaining case having been dealt with in our paper: On the Diophantine equation 1+ X + Y = Z, This work extends earlier work of the authors in the field of exponential Diophantine equations.

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On the basic character of residue classes.

Peter J. Hilton, Jennifer Hooper, Jean Pedersen (1989)

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Let t, b be mutually prime positive integers. We say that the residue class t mod b is basic if there exists n such that t ≡ -1 mod b; otherwise t is not basic. In this paper we relate the basic character of t mod b to the quadratic character of t modulo the prime factors of b. If all prime factors p of b satisfy p ≡ 3 mod 4, then t is basic mod b if t is a quadratic non-residue mod p for all such p; and t is not basic mod b if t is a quadratic residue mod p for all such p. If, for all...