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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- Apr 29th 2012, 02:54 AMalexandrabel90coprime
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 - Apr 29th 2012, 05:39 AMigniteRe: coprime
Let your numbers be a and a+1 and their gcd be d.

$\displaystyle \Rightarrow d | a $ and $\displaystyle d | a+1 \Rightarrow d | (a+1-a) \Rightarrow d | 1 \Rightarrow d=1$ - Apr 29th 2012, 09:18 AMSylvia104Re: Coprime
To show that two integers $\displaystyle m,n$ are coprime, it is sufficient to find integers $\displaystyle r,s$ such that $\displaystyle rm+sn=1$ (because any common divisor of $\displaystyle m,n$ must divide $\displaystyle rm+sn$ for all integers $\displaystyle r,s).$ In the case $\displaystyle m=a,$ $\displaystyle n=a+1,$ you have $\displaystyle n-m=1;$ hence $\displaystyle \gcd(m,n)=1.$