數學知識交流---勾股弦關係

a = 2pmn, b=p(m² - n²), c = p(m² + n²)
因為 m > n, 若 2pmn = 201202 = 2*29*3469, 則
(p, m, n) . . . . . [ 2pmn, p(m² - n²), p(m² + n²)]
= (1, 100601, 1) . . [201202, 10120561200, 10120561202]
= (1, 3469, 29) . . [201202, 12033120, 12034802]
= (29, 3469, 1) . . [201202, 348984840, 348984898]
= (3469, 29, 1) . . [201202, 2913960, 2920898]
若 p(m² - n²) = p(m + n)(m - n) = 201202 = 2*29*3469, 則
(p, m, n) . . . . . [ 2pmn, p(m² - n²), p(m² + n²)]
= (2, 50301, 50300). [10120561200, 201202, 1012056102]
= (2, 1749, 1720) . [ 12033120, 201202, 12034802]
若 p(m² + n²) = 201202 = 2*29*3469, 則
(p, m, n) . . . . . [ 2pmn, p(m² - n²), p(m² + n²)]
= (1, 429, 131) . . [112398, 166880, 201202]
= (1, 401, 201) . . [161202, 120400, 201202]
= (2, 280, 149) . . [166880, 112398, 201202]
= (2, 301, 100) . . [120400, 161202, 201202]
= (29, 83, 7) . . . [ 33698, 198360, 201202]
= (58, 45, 38) . . . [198360, 33698, 201202]
= (3469, 7, 3) . . . [145698, 138760, 201202]
= (6938, 5, 2) . . . [138760, 145698, 201202]
所以 201202 的勾股數組有 : (a < b < c)
( 33698, 198360, 201202);
(112398, 166880, 201202);
(120400, 161202, 201202);
(138760, 145698, 201202);
(201202, 2913960, 2920898);
(201202, 12033120, 12034802);
(201202, 348984840, 348984898);
(201202, 10120561200, 10120561202) 八組.