This exercise presents another proof that there are infinitely many primes. Assume that th...

This exercise presents another proof that there are infinitely many primes. Assume that there are exactly r primes p1p2,…, pr. Let  for k = 1,2,…, r. Let . Show that S must have a prime factor not among the r primes listed. Conclude that there are infinitely many primes. (This proof was published by G. Métrod in 1917.)