What is "congruum"

In number theory, a congruum (plural congrua) is the difference between successive square numbers in an arithmetic progression of three squares. That is, if x, y, and z (for integers x, y, and z) are three square numbers that are equally spaced apart from each other, then the spacing between them, , is called a congruum.

The congruum problem is the problem of finding squares in arithmetic progression and their associated congrua. It can be formalized as a Diophantine equation: find integers x, y, and z such that

y − x = z − y.
When this equation is satisfied, both sides of the equation equal the congruum.

Fibonacci solved the congruum problem by finding a parameterized formula for generating all congrua, together with their associated arithmetic progressions. According to this formula, each congruum is four times the area of a Pythagorean triangle. Congrua are also closely connected with congruent numbers: every congruum is a congruent number, and every congruent number is a congruum multiplied by the square of a rational number.