一道英文数学题There is a positive integer,B,such that 2B is a perfe

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一道英文数学题
There is a positive integer,B,such that 2B is a perfect square,3B is a perfect cube,and
5B is a perfect fifth (an integer to the fifth power).Assume that B is the smallest such
number.How many factors are in the prime factorization of

题目翻译过来：求一个最小的正整数数B,乘2是一个完全平方数,乘3是一个完全立方数,乘5是一个完全五次方数.那么在B的质因数中有多少个因子?
答案：因为2*B是完全平方数,所以B含有2^(x),x为正奇数；
因为3*B是完全立方数,所以B含有3^(y),y=3*n-1,n为正整数；
因为5*B是完全五次方数,所以B含有5^（z）,z=5*m-1,m为正整数.
综上所述：B是包含2、3、5三个质数因子,B=2^(x)*3^(y)*5^（z）,
其中x是正奇数,且x是3、5的倍数,取最小值x=15；
y=3*n-1,n为正整数,且y是2、5的倍数,取最小值y=20；
z=5*m-1,m为正整数,且z是3、2的倍数,取最小值z=24；
故最小的自然数B=2^(15)*3^(20)*5^(24)

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