2. 外语
  3. Both m and n are positive integers greater than 1.If 23(m-2)=21(n-3)，what is the least possible value of m+n?

Both m and n are positive integers greater than 1.If 23(m-2)=21(n-3)，what is the least possible value of m+n?

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问题 Both m and n are positive integers greater than 1.If 23(m-2)=21(n-3)，what is the least possible value of m+n?
选项 A、98
B、49
C、22
D、24
E、26
答案B
解析 23(m-2)=21(n-3)，由于21和23互质，根据性质3，n-3必然含有因子23，m-2必然含有因子21，那么m最小值为21+2=23，n最小值为23+3=26，所以m+n的最小值为49。正确答案为B。
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