Past exam of the options I course of the University of Oxford / 2004 / C / C1 / a / i

By the fundamental theorem of arithmetic, every integer greater than one has a prime factorization, and that factorization is unique up to reordering the factors. Equivalently, it has a unique finite prime-exponent representation $\boxed{n=\prod _p{p}^{v_p(n)}}$, with nonnegative integer exponents. The unit integer has the empty product.