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一组勾股弦(整)数a、b、c中,必有含因子3的数,必有含因子4的数;必有含因子5的数。 如6、8、10是一组(整)勾股数组,其中3|6,4|8,5|10。 又如7、24、25是一组(整)勾股数组,其中3|24,4|24,5|25。 为了证明这个事实,我们先来证明这样一个定理。任何一组勾股(整)数组a、b、c组可由公式a=m~2-n~2,b=2mn,c=m~2+n~2表示。(这里m>n,m、n均为自然数)(参看马明同志著《圆和二次方程》P_(27))
In a group of ticks (integer) numbers a, b, and c, there must be a number containing factor 3, there must be a number containing factor 4, and there must be a number containing factor 5. For example, 6, 8, and 10 are a set of (complete) Pythagorean arrays, of which 3|6, 4|8, 5|10. Again, for example, 7, 24, 25 is a set of (complete) Pythagorean arrays, of which 3|24, 4|24, 5|25. In order to prove this fact, we first prove such a theorem. The group a, b, and c of any group of gouache (entire) arrays can be represented by the formula a=m~2-n~2, b=2mn, c=m~2+n~2. (here m>n, m and n are natural numbers) (see Comrade Ma Ming’s “Circular and Quadratic Equations” P_ (27))