Squares of form 2 n^2 - 1

Theorem

The sequence of integers $\left\langle{n}\right\rangle$ such that $2 n^2 - 1$ is square begins:

$1, 5, 29, 169, 985, 5741, 33461, 195025, 1136689, 6625109, \ldots$

This sequence is A001653 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Proof


This theorem requires a proof.
In particular: Follows somehow from the fact that these numbers are the hypotenuses of Definition:Almost Isosceles Pythagorean Triangles.
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Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $29$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $29$
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