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 UN cargo (Posted on 2013-03-13)
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?

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 answer Comment 9 of 9 |

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

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