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

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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(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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     title = {Numbers {Differing} from {Consecutive} {Squares} by {Squares}},
     journal = {Canadian mathematical bulletin},
     pages = {337--342},
     year = {1985},
     volume = {28},
     number = {3},
     doi = {10.4153/CMB-1985-040-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-040-9/}
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