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I want to know, if is possible found the arithmetic progression of four square number, with the same common difference.

\begin{align} \ & a^2 +r = b^2 \\ & b^2 +r = c^2 \\ & c^2 +r = d^2 \\ \end{align}

where a,b,c,d,r $\in\mathbb{N}$

Hence, I found only triple succession.

For example: 1,5,7 because \begin{align} \ & 1^2 +24 = 5^2 \\ & 5^2 +24 = 7^2 \\ \end{align} where the ratio is 24.

but I can't found a example with four number and the same common difference. at worst. Could you demonstrate that nonexistent using reductio ad absurdum to this statement?.

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  • $\begingroup$ It's usually called a common difference, not a ratio. $\endgroup$ – steven gregory Oct 13 '17 at 8:34
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    $\begingroup$ Ok, but I'm just learning English. Thanks for your comment $\endgroup$ – Juan Alfaro Oct 13 '17 at 8:37