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Math Help - Congruence of + integer?

  1. #1
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    Congruence of + integer?

    Prove that (x+1)(x+2)(x+k) ≡0 (mod k) for all integers x given that k is a + integer.
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  2. #2
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    Re: Congruence of + integer?

    x+1, x+2,..., x+k are k successive integers in a row. since the multiples of k occur every k integers, at least one (in fact, exactly one) of the x+somethings is a multiple of k.

    thus the whole product is a multiple of k, which is to say, congruent to 0 mod k.
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