论文部分内容阅读
9.费马大方程。 在()+()=()中,填 三个自然数,使等式成立,这很容 易,左边括号任写两个自然数,求 出和填在右边括号中,就行了。但填()~2十()~2=()~2就比较困难了,可以想出3~2+4~2=5~2,5~2+12~2=13~2,7~2+24~2=25~2等,这实际上就是有名的勾股定理。 那么在()~3+()~3=()~3,()~4+()~4=()~4,()~5+()~5=()~5……中应填什么数呢?也就是当n≥3时,x~n+y~n=z~n有正整数解吗?这个问题早在1670年就正式被提出,虽然当时的大数学家费马声称,这个不定方程没有正整数解,他本人也
Fermat large equation. In () + () = (), fill in three natural numbers to make the equation hold. It is easy. Let's write two natural numbers to the left of the parentheses. But it is difficult to fill () ~ 2 ~ () ~ 2 = () ~ 2, we can think of 3 ~ 2 + 4 ~ 2 = 5 ~ 2,5 ~ 2 + 12 ~ 2 = 13 ~ 2,7 ~ 2 +24 ~ 2 = 25 ~ 2, which is actually the famous Pythagorean theorem. Then in () ~ 3 + () ~ 3 = () ~ 3, () ~ 4 + () ~ 4 = () ~ 4, () ~ 5 + That is, when n≥3, does x ~ n + y ~ n = z ~ n have a positive integer solution? This problem was formally proposed as early as 1670, although the then great mathematician Fei Ma claimed This indefinite equation has no positive integer solution, he himself