昌爸那邊的題目
請證明勾股數必為60的倍數
我看過siuhochung的解法.
我有更好的解法.只需因式分解即可
一起討論吧!
[數學]勾股數組
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由 kevin 於 星期日 五月 11, 2003 11:35 am
轉貼自昌爸234fermat:
a=k(m^2-n^2)
b=2kmn
c=k(m^2+n^2)
2k^3 mn (m^2-n^2)(m^2+n^2)
Smallest case
2mn(m-n)(m^2+n^2)
if m or n =0(mod 2), then the product is divisible by 4.
Else both of them are odd, m-n =0(mod 2), the product is divisible by4.
If m or n=0(mod 3), the product is divisible by 3.
If m=n(mod 3), the product is divisible by 3.
If m=1, n=2(mod 3) or m=2 n=1(mod 3), 3｜m^2+n^2, the product is divisible
by 3.
Similar for proving divisible by 5
a=k(m^2-n^2)
b=2kmn
c=k(m^2+n^2)
2k^3 mn (m^2-n^2)(m^2+n^2)
Smallest case
2mn(m-n)(m^2+n^2)
if m or n =0(mod 2), then the product is divisible by 4.
Else both of them are odd, m-n =0(mod 2), the product is divisible by4.
If m or n=0(mod 3), the product is divisible by 3.
If m=n(mod 3), the product is divisible by 3.
If m=1, n=2(mod 3) or m=2 n=1(mod 3), 3｜m^2+n^2, the product is divisible
by 3.
Similar for proving divisible by 5
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kevin - 教 授
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