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SOME OBSERVATIONS ON THE DIOPHANTINE EQUATION y2=x!+A AND RELATED RESULTS
Published online by Cambridge University Press: 02 August 2012
Abstract
We consider the Brocard–Ramanujan type Diophantine equation y2=x!+A and ask about values of A∈ℤ for which there are at least three solutions in the positive integers. In particular, we prove that the set 𝒜 consisting of integers with this property is infinite. In fact we construct a two-parameter family of integers contained in 𝒜. We also give some computational results related to this equation.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 86 , Issue 3 , December 2012 , pp. 377 - 388
- Copyright
- Copyright © Australian Mathematical Publishing Association Inc. 2012
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