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 by Charlie)

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.

Posted by Ady TZIDON on 2015-09-03 03:32:58