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Math Help - gcd, lcm

  1. #1
    Sea
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    gcd, lcm

    a\in\mathbb{Z^{+}} (a,a+1)=? , [a,a+1]=? (proof)
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  2. #2
    o_O
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    #1: Let d = (a, a+1) \geq 1. This means that d \mid a and d \mid (a+1).

    Fact: If d \mid x and d \mid y, then  d \mid (x+y).

    This means that  d \mid \left[(a+1) - a\right] \ \Leftrightarrow \ d \mid 1.

    So d = \cdots

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    #2: Use the fact that if (a,b) = 1 then [a,b] = ab
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