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Say I have three square numbers

(these are squared whole numbers greater than ZERO)

S1 < S2 < S3

how would you go about showing that the following is possible

S2 - S1 = S3 - S2

e.g. the difference between S1 and S2 is the same as that between S2 and S3

Akababa
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Hector
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    It's not true for 1,4,9 – Akababa Jun 08 '17 at 15:08
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    $9-4\ne 4-1{}{}{}$ – peterwhy Jun 08 '17 at 15:09
  • I agree, is it true for any set of three squared numbers? – Hector Jun 08 '17 at 15:10
  • untrue for all sets of squares – Saketh Malyala Jun 08 '17 at 15:13
  • duplicate of (https://math.stackexchange.com/q/43519) – Jean Marie Jun 08 '17 at 15:33
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    You should think carefully about your question and phrasing it. It often helps you answer your own question. To show it is possible just takes one case. Did you want to know if there are infinite classes of solutions? – Ross Millikan Jun 08 '17 at 15:40
  • Thanks for your advice. My enthusiasm for maths got the better of me. What I actually need are two pairs of squares that are equi distance "Before" and "After" a "central" square. the distance refers to the difference between the squares and the pivot square. e.g. I need the difference between S2 and S1 to be identical to the difference between S3 and S2. the squares involved do not have to be consecutive. – Hector Jun 08 '17 at 15:46

1 Answers1

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The sequence $1^2,5^2,7^2$ works.

For more solutions you can take $(m^2+2mn-n^2)^2,(m^2+n^2)^2,(n^2+2mn-m^2)^2$ for $n>m$.

Akababa
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