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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.

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  • $\begingroup$ Hint: $\gcd(a,b) = \gcd(a,a+b) = \gcd(a,20)$. $\endgroup$ – Erick Wong Oct 17 '17 at 7:01
  • $\begingroup$ @ErickWong The question has been solved i think $\endgroup$ – ami_ba Oct 17 '17 at 7:03
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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 $p\neq 2,5$.

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    $\begingroup$ You don't even need $p$ prime, just $\gcd(p,20)=1$. $\endgroup$ – Daniel Schepler Oct 17 '17 at 6:58
  • $\begingroup$ @DanielSchepler Understood $\endgroup$ – ami_ba Oct 17 '17 at 6:59

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