For all positive integers n, r, and s, if rs ≤ n, then r≤ √n or or s

For what values of c is c(1,2,3)=1?

Find the smallest integer in the given set. { and for some in } { and for some in }

Let a,b,c and d be integers such that ab and cd. Prove that acbd.

Let and be positive integers. If and is the least common multiple of and , prove that . Note that it follows that the least common multiple of two positive relatively prime integers is their product.

20. If and are nonzero integers and is the least common multiple of and prove that.

Prove that if and are integers such that and , then .