Congruum

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

[edit] References

• Congruum at Mathworld