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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?
admin
2022-12-19
23
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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