# coprime

• April 29th 2012, 02:54 AM
alexandrabel90
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
• April 29th 2012, 05:39 AM
ignite
Re: coprime
Let your numbers be a and a+1 and their gcd be d.
$\Rightarrow d | a$ and $d | a+1 \Rightarrow d | (a+1-a) \Rightarrow d | 1 \Rightarrow d=1$
• April 29th 2012, 09:18 AM
Sylvia104
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 $\gcd(m,n)=1.$