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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''2, ''y''2, and ''z''2 (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 : 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. == Examples == For instance, the number 96 is a congruum, since it is the difference between each pair of the three squares 4, 100, and 196 (the squares of 2, 10, and 14 respectively). The first few congrua are: :24, 96, 120, 216, 240, 336, 384, 480, 600, 720 … . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「congruum」の詳細全文を読む スポンサード リンク
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