# Can I prove that there are infinitely many solutions for co primes $(a,b)$ to $a+b=20$?

Can I prove that there are infinitely many solutions for co primes $(a,b)$ to $a+b=20$?

This is an intermediate step of another problem. I know that there will be infinitely many integer solutions(Diophantine) but I can not prove (or disprove) that there will be for co primes.

• Hint: $\gcd(a,b) = \gcd(a,a+b) = \gcd(a,20)$. – Erick Wong Oct 17 '17 at 7:01
• @ErickWong The question has been solved i think – ami_ba Oct 17 '17 at 7:03

You can always take a prime $p$ and set $a=p, b=20-p$ and you will end up with $a,b$ coprime so long as $p\neq 2,5$.
• You don't even need $p$ prime, just $\gcd(p,20)=1$. – Daniel Schepler Oct 17 '17 at 6:58