Suppose m n N Explain why nm impliies n lessthanorequalto m

Suppose m, n N. Explain why n|m impliies n lessthanorequalto m b) Suppose n, m Z and that both n|m and m|n. Prove that either m = n or m = - n.

Solution

a) Given n|m so m=kn for k=1,2,3,4,....

i.e., m is a multiple of n

minimum value of m is m = 1.n when k=1 i.e., m=n

the value m increases with increase in k

so m>n

from the two equations

m>=n or n<=m