x、y、z均为整数,且11|7x+2y-5z,求证:11|3x-7y+12z.
人气:429 ℃ 时间:2019-08-20 21:45:29
解答
∵11整除7x+2y-5z,∴11整除(7x+2y-5z)×2,∵(7x+2y-5z)×2=14x+4y-10z,∵x、y、z均为整数,∴x+y-2z为整数,∴11整除11×(x+y-2z),∵11×(x+y-2z)=11x+11y-22z,∴(7x+2y-5z)×2-11×(x+y-2z)=3x-7y...
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