Question

一个数被5除余2,被7除余6,被11除余9,这个数是几? 我要过程!

Answer 1

设此数N=5a+2=7b-1=11c-2, a,b,c都为整数

则有：a=(7b-3)/5=b-1+2(b+1)/5, 则b+1须整除5,

令b+1=5t, 则b=5t-1, a=7t-2

故N=5a+2=35t-8=11c-2

c=(35t-6)/11=3t+2(t-3)/11, 则t-3须整除11,

令t-3=11k, 则t=11k+3

则N=35t-8=35(11k+3)-8=385k+97, k为任意整数