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
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 $n>m$.