=+5.19. 2.181 For integers m and primes p, let @ (m) be the exact power of p in the prime factorization of m: m = II ,pap(m). Let 8 (m) be 1 or 0 as p divides m or not. Under each P ,, (see (2.34)) the @, and 8, are random variables. Show that for distinct primes pt, . . . , Pur

(5.43)

P.[ ap, zk, isu] = n 1

and P.[ap, = k, isu] > [](pp)

(5.44)

Similarly, P.160= 1,isu]-|0."[]→

1

(5.45)

Pitt. Pu