Well, Pythagorean triples are given by
for integers and with (to prove that these are all is irrelevant; we only need infinitely many triples, not necessarily all of them).
So let and an odd ', then we have the triple . The corresponding would then be (since for ), this is an irreducible fraction if we divide both sides by (that is , and this is irreducible because and are co') and so it's different for every . Since there are infinitely many 's , the set is infinitely large (it actually contains a lot more numbers than we've shown, but that is irrelevant for it infinite-ness).
Not exactly what you’re looking for?