# Tag Info

## New answers tagged arithmetic-progression

28

The answer is yes. Here is another example, $$x=2021231^2, \qquad d=82153503191760.$$ Then $$x+d=9286489^2, \qquad x+2d=12976609^2, \qquad x+4d=18240049^2.$$ Basically, write $x=X^2$, $x+d=Y^2$, $x+2d=Z^2$, and $x+4d=W^2$. Eliminating $x$ and $d$ reduces to the two equations: $$X^2-2Y^2+Z^2=0, \qquad 3X^2-4Y^2+W^2=0.$$ This pair of equations defines a ...

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