Congruum

Congruum
For the female singular in ecclesiastical context, see congrua portio.

A congruum (plural congrua) is a positive integer h which results in a square integer when added or subtracted from some square integer. For instance, the number 96 is a congruum, since

102 − 96 = 4 = 22

and

102 + 96 = 196 = 142

Formally, we may defined congrua as those integers h for which there exist integers x, a and b such that

x2 + h = a2

and

x2 − h = b2.

The first few congrua (sequence A057102 in OEIS) are: 24, 96, 120, 240, 336, 384, 480, 720, 840, 960 ... .

References


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