余数--32数学JJ

crack25

1.五个数被5除之后的余数都是不一样的，问一下哪些被五除之后的余数都不一样
有2a,2b,2c,2d,2e;2+a,2+b,2+c,2+d,2+e;a^2,b^2,c^2,d^2,e^2
知道最后一个不行，但是求助能给出理论分析吗？而不是代数进去

sdcar2010

2+a,2+b,2+c,2+d,2+e

This must work since each remainder is changed to plus 2 and they are not equal, either.

2a,2b,2c,2d,2e

Suppose we have remainders of 1, 2, 3, 4, 0 for a to e. Then for 2a, 2b .. 2 e the remainders become 2, 4, 1, 3, 0.  Still not equal.

Following the same line of thinking, for a^2,b^2,c^2,d^2,e^2, the remainders become 1, 3, 4, 1, 0.  Not working any more due to the presence of two 1's.

心诚则灵的MM

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