Find the prime factorization of (cid:18)20 (cid:19) (a) 8400; (b) 10! (c) 10 (a) 8400 = 84 100 = (4 21) (4 25) = 24 3 52 7. (b) 10! 11 12 13 14 15 16 17 18 19 20. 2 3 4 5 6 7 8 9 10. = 22 11 13 17 19, as is easily obtained after some cancellations. l. The number (20: is an example of a binomial coef cient. To learn more on this, check out a separate le to be posted under practice exercises and optional reading . Prove that for any a, b p n, if an | bn for some n p n, then a | b. Consider the prime factorizations of a and b, given by a = p 1.
