Thread: [SOLVED] Help With Proofs

Hey, could I get receive some help with these problems, thanks.

1) Show that p is a prime number and p divides the product ab then a divides a or b divides b.
2) Let Tn be the highest power of 2 that divides n. Show that Tnm = Tn + Tm
3) Let n, c, and d be three integers. Show that if d * c divides n * c then d divides n.

Originally Posted by Tom.O

Hey, could I get receive some help with these problems, thanks.

1) Show that p is a prime number and p divides the product ab then a divides a or b divides b.
2) Let Tn be the highest power of 2 that divides n. Show that Tnm = Tn + Tm
3) Let n, c, and d be three integers. Show that if d * c divides n * c then d divides n.

Do you know the Fundamental Theorem of Arithmetic? These all follow from
it with only a little work.

ZB

Originally Posted by Constantine11

Do you know the Fundamental Theorem of Arithmetic? These all follow from
it with only a little work.

We cannot use the factorization theorem. Because the proof of it is based on proving #1. And we cannot use a result to prove a result that is used to prove it.

Originally Posted by Tom.O

1) Show that p is a prime number and p divides the product ab then a divides a or b divides b.

If p|a then proof is complete, otherwise gcd(a,p)=1 but then p|b.