(1)
(2)
Solution to (1) :
Take any set of three squares in arithmetic progression
Let’s take for the three squares, and let the common difference be .
The solution is obtained by giving the value
and
Here’s an example :
, ,
Solution of (2) : The method is similar to that in (1)
The first pair (p,x) where x*(x ± p) both are squares is (24,25).
Other pairs are of course (48, 50), (72,75) etc, n times the primitive solution.
Other primitive pairs (p,x) are:
(120, 169)
(240, 289)
(336, 625)
(720, 1681)
(840, 841)
(840, 1369)
(1320, 3721)
(2016, 4225)
(2184, 7225)
(2520, 2809)
(3696, 4225)
(5280, 5329)
(5544, 7225)
(6240, 7921)
(9360, 9409)
pipo
Here’s my solution to part (1)