Geodesic
Numbers Differing from Consecutive Squares by Squares
Canadian mathematical bulletin, Tome 28 (1985) no. 3, pp. 337-342

Voir la notice de l'article provenant de la source Cambridge University Press

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(b 2 + 1) = a 2 + c 2. 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.
DOI : 10.4153/CMB-1985-040-9
Mots-clés : 10B05 
Barbeau, E. J. Numbers Differing from Consecutive Squares by Squares. Canadian mathematical bulletin, Tome 28 (1985) no. 3, pp. 337-342. doi: 10.4153/CMB-1985-040-9
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