2. You may have seen in a previous class Euclid’s proof that there are infinitely many prime integers: Given any finite list of primes pi, p2… pn, the integer pi • • • pn 1 is not divisible by any of them. Keeping in mind that K[x] is a PID (and therefore a UFD) for any field K, adapt this argument to show that there are infinitely many monic irreducible polynomials in K[x].
