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

W. Ljunggren (1972)

Acta Arithmetica

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W. Ljunggren (1972)

Acta Arithmetica

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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.

A. Rotkiewicz (1983)

Acta Arithmetica

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Cosgrave, John B., Dilcher, Karl (2008)

Integers

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

Publicacions Matemàtiques

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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...

Dilcher, Karl, Skula, Ladislav (2006)

Integers

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Abu Muriefah, Fadwa S. (2001)

International Journal of Mathematics and Mathematical Sciences

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Granville, Andrew (2004)

Integers

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Gica, Alexandru, Panaitopol, Laurenţiu (2003)

Journal of Integer Sequences [electronic only]

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Hudson, Richard H., Williams, Kenneth S. (1982)

International Journal of Mathematics and Mathematical Sciences

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Robert Tichy, G. Turnwald (1985)

Acta Arithmetica

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