朋友考试，放一题数学狗，求讨论！

kishi6 · 发表于 2015-8-26 18:07:27

m,n都是正整数，问m^n是否是perfect square
1,m 是perfect square
2.n 是perfect square
perfect square是完全平方的意思？这个题咋做。。。。

Polyanthus · 发表于 2015-8-26 18:42:43

Tips about the perfect square:
1. The number of distinct factors of a perfect square is ALWAYS ODD. The reverse is also true: if a number has the odd number of distinct factors then it's a perfect square;

2. The sum of distinct factors of a perfect square is ALWAYS ODD. The reverse is NOT always true: a number may have the odd sum of its distinct factors and not be a perfect square. For example: 2, 8, 18 or 50;

3. A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors. The reverse is also true: if a number has an ODD number of Odd-factors, and EVEN number of Even-factors then it's a perfect square. For example: odd factors of 36 are 1, 3 and 9 (3 odd factor) and even factors are 2, 4, 6, 12, 18 and 36 (6 even factors);

Polyanthus · 发表于 2015-8-26 18:43:29

－－－－－－－－－－－－－－

brianmay · 发表于 2015-8-26 18:56:43

A吧，
条件1.设m=a^2，转化为 (a^2)^n=(a^n)^2 ,ok
条件2不行

朋友考试，放一题数学狗，求讨论！

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