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Related to this question : Find three arithmetic progressions of three square numbers

I am looking for a sequence $$a_1,a_2,\cdots a_n$$ forming an arithmetic progression such that all the $a_j$ are perfect squares, an example with $3$ entries is $$49,169,289$$ However, the next term would be $409$ , not being a perfect square.

Can the index $n$ be aqrbitary large ? In other words, can the sequence be arbitary long ? If not, what is the maximum possible value for $n$ ?

Peter
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    No, there can't be more than three squares in arithmetic progression. This question has been asked, and answered, several times on this website. Let's try to find it. – Gerry Myerson Oct 14 '17 at 08:25
  • @GerryMyerson What is the main idea to prove that $3$ is the maximum ? – Peter Oct 14 '17 at 08:27

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