x、y、z均为整数，且11|7x+2y-5z，求证：11|3x-7y+12z．

∵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...