牛人帮我解答一下这道数学题吧！我一点思路都没有！

zt1127

If the integer n has exactly three positive divisors, including 1 and n, How many positive divisor does n^2 have?
小女子在这里叩谢各位神人！

二丫zheng

If the integer n has exactly three positive divisors, including 1 and n, How many positive divisor does n^2 have?
小女子在这里叩谢各位神人！

-- by 会员 zt1127 (2011/6/30 20:10:53)

不是神人，但这题我在上xdf的时候，老师说过
如果一个数N有奇数个因子，那么N为平方数即4、9、16、25……
这样，假设N=4，那么N^2=16=2^4,则N^2有5个因子

sdcar2010

If the integer n has exactly three positive divisors, including 1 and n, How many positive divisor does n^2 have?

If the integer n has exactly three positive divisors, including 1 and n, then n is a square of another integer m, or n=m*m. In this way, n, or m^2, has three positive divisors: 1, m, and m^2.

Then n^2, which is m^4, will have 1, m, m^2, m^3, and m^4, 5 divisors or factors.