Stella octangula number

In mathematics, a stella octangula number is a figurate number based on the stella octangula, of the form n(2n² − 1).

The sequence of stella octangula numbers is

There are only two positive square stella octangula numbers, 1 and 9653449 = 3107² = (13 × 239)², corresponding to n = 1 and n = 169 respectively. The elliptic curve describing the square stella octangula numbers,

may be placed in the equivalent Weierstrass form

by the change of variables x = 2m, y = 2n. Because the two factors n and 2n² − 1 of the square number m² are relatively prime, they must each be squares themselves, and the second change of variables ${\displaystyle X=m/{\sqrt {n}}}$ and ${\displaystyle Y={\sqrt {n}}}$ leads to Ljunggren's equation

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