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Prime producing polynomials: Proof of a conjecture by Mollin and Williams

100%

Srinivasan A.

Acta Arithmetica

1999

tom 89

nr 1

1-7

On fundamental solutions of binary quadratic form equations

51%

Matthews K., Robertson J., Srinivasan A.

Acta Arithmetica

2015

tom 169

nr 3

291-299

We show that, with suitable modification, the upper bound estimates of Stolt for the fundamental integer solutions of the Diophantine equation Au²+Buv+Cv²=N, where A>0, N≠0 and B²-4AC is positive and nonsquare, in fact characterize the fundamental solutions. As a corollary, we get a corresponding result for the equation u²-dv²=N, where d is positive and nonsquare, in which case the upper bound estimates were obtained by Nagell and Chebyshev.

Ograniczanie wyników

2 Acta Arithmetica

2 Srinivasan A.

1 Matthews K.

1 Robertson J.

1 2015

1 1999

Wyniki wyszukiwania

Prime producing polynomials: Proof of a conjecture by Mollin and Williams

On fundamental solutions of binary quadratic form equations