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.

  • $\begingroup$ 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

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 $p\neq 2,5$.

  • 4
    $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.