A triplet (1,25,49) represents 3 perfect squares forming an arithmetic progression.

1. Provide few additional samples like the above.
2. What can be said about the possible values of d (the constant
difference between the adjacent members of an arithmetic progression)?
3. How relates the title of my post to its contents?

So others do not need to search the OEIS for the word:

A congruum (plural: congrua, an anagram of UN cargo) is defined as a positive integer which when added to and subtracted from a positive square integer results in positive square integers.

Not all positive squares have an associated congruum.
The smallest congruum is 24 with the square of 5 (25):
 5² - 24 = 1²  and 5² + 24 = 7²

All known congrua are some multiple of 24. Not all multiples of 24 are congrua.

96 = 4·(24):
10² + 96 = 14²  and 10² - 96 = 2²

120 = 5·(24):
13² + 120 = 17²  and 13² - 120 = 7²

Posted by Dej Mar on 2013-03-14 11:32:08