Number theory and other reminiscences of Viscount Cherwell

Abstract

Lord Cherwell (i) was, of course, a very distinguished ex-perimental physicist but he had (like many others) a considerable active interest in the theory of numbers. I met him in 1930 when Christ Church, Oxford, elected me to a Senior (postgraduate) Scholarship and I migrated there from my original college. Cherwell’s first published work (2) in the theory of numbers was a very simple and elegant proof of the fundamental theorem of arithmetic, that any positive integer can be expressed as a product of prime numbers in just one way (apart from a possible rearrangement of the order of the factors). (A prime is a positive integer greater than 1 whose only factors are 1 and itself.) His proof is by the method of descent (used by Fermat, but not for this problem). Assume the fundamental theorem false and call any number that can be expressed as a product of primes in two or more ways abnormal.