perplexus.info :: Sequences : One square implies many

One square implies many (Posted on 2018-03-28)

Prove the following:
If there is one perfect square in an arithmetic progression, then there are infinitely many.

No Solution Yet Submitted by Ady TZIDON

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quite easy solution for integers

| Comment 5 of 6 |

if a^2 belongs to an arithmetic progression with ratio m (and m is a positive integer (see Steve Herman and broll)

Then the squares of a+m, a+2m, ... a+km ... belong to the sequence

(a+km)^2= a^2+m*(mk^2+2ak)

========

Ramdom ex:

a^2=36 m=13 k=5

(6+13*5)^2=71^2=5041=36+385*13

Edited on March 28, 2018, 2:13 pm

Posted by armando on 2018-03-28 12:46:26

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