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华罗庚著《数論导引》中“商高定理”一节,見有方程 x~2+y~2+z~2=w~2 (1)习題一则,遂默思其解,得到了解法数种。現在写出来向同志們請教。 (一) 我們称方程 x~2+y~2=z~2 (2)的解[x,y,z]为“商高数”。如有两組商高教,其一組之第三項(或其倍数)适与另一組之第一或第二項(或其倍数)相等,以第一組之前两項,代另一組之前两項中之一項,那么,就得到方程(1)的一組解。设两組商高数:
Hua Luogeng’s “Theorem of Propositions” in the “Theory of Number Theory” section, see equation x~2+y~2+z~2=w~2 (1) Problem 1 , meditation on the solution, get Learn a few ways. Now write up and ask the comrades. (a) We call the solution [x,y,z] of the equation x~2+y~2=z~2 (2) the “quotient of quotients.” If there are two groups of higher education, the third (or multiple) of the group is equal to the first or second (or multiple) of the other group. One of the two previous terms, then, a set of solutions to equation (1) is obtained. Set two groups of high numbers: