P,Q,R and S are four positive integers in arithmetic sequence, with P < Q < R < S.
Find all possible solutions such that:
P3 + Q3 + R3 + S3 is a perfect square.
(In reply to computer exploration
Since each off the listed solutions is a generic one and each quadruplet multiplied by k^2 produces another valid solution,- the request "Find all possible solutions..." is a priori impossible to achieve.
This fact, regretfully, escaped the attention of all who saw this puzzle (myself included) on the review board.
Let us be more vigilant in the future.