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

Question

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.

Answer 1

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 $p\neq 2,5$.