The product of the first n of this person’s numbers equals the n plus first of their numbers minus two, from which it follows there are infinitely many primes. A theorem of this mathematician can be proven by forming necklaces with coloured beads and excluding necklaces that are formed of the same colour. A corollary of one of this mathematician’s theorems states that if an integer can be written as the sum of (*) two squares in two different ways, (-5[1])then that integer (10[1])is composite. Composite numbers satisfying one of this person’s theorems are named for Carmichael. (10[2])The Taniyama-Shimura conjecture was the final obstacle to proving a theorem by this mathematician. Euler’s Totient Theorem generalises their “little theorem”. For 10 points, Andrew Wiles proved what mathematician’s ‘last theorem’? ■END■