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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

\( 10^2-96 = 4 = 2^2 \)

and

\( 10^2+96=196=14^2 \)

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

\( x^2+h=a^2 \)

and

\( x^2-h=b^2. \)

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

Congruum at Mathworld

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