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Math Help - coprime

  1. #1
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    coprime

    how do you show that 2 consecutive integers are coprime?

    i know we need to show that gcd is 1 where they have opp parity
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  2. #2
    Junior Member ignite's Avatar
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    Re: coprime

    Let your numbers be a and a+1 and their gcd be d.
     \Rightarrow d | a and  d | a+1 \Rightarrow d | (a+1-a) \Rightarrow d | 1 \Rightarrow d=1
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  3. #3
    Member Sylvia104's Avatar
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    Re: Coprime

    To show that two integers m,n are coprime, it is sufficient to find integers r,s such that rm+sn=1 (because any common divisor of m,n must divide rm+sn for all integers r,s). In the case m=a, n=a+1, you have n-m=1; hence \gcd(m,n)=1.
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