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Numbers Differing from Consecutive Squares by Squares

Published online by Cambridge University Press:  20 November 2018

E. J. Barbeau
E. J. Barbeau*
Affiliation:
University of Toronto, Toronto, M5S 1A1
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Abstract

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It is shown that there are infinitely many natural numbers which differ from the next four greater perfect squares by a perfect square. This follows from the determination of certain families of solutions to the diophantine equation 2(b2 + 1) = a2 + c2. However, it is essentially known that any natural number with this property cannot be 1 less than a perfect square. The question whether there exists a number differing from the next five greater squares by squares is open.

Keywords

10B05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 3 , 01 September 1985 , pp. 337 - 342
Copyright
Copyright © Canadian Mathematical Society 1985

References

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