Quick number theory clarification before exam

[chimath35]

I'm currently taking an Intro to Proofs course after going through an undergrad in physics and math with a phobia of proofs and it's helped a lot.

If you're interested in getting better at proofs I would recommend learning some basic proof techniques (it might be useful to learn some logic beforehand). The most common techniques you'll use are direct, contrapositive, contradiction, and induction.

The problem we're discussing here and the proof outline I provided were using a direct proof.

Unfortunately, the only way to get better at doing proofs is to do a bunch of proofs. If your exam is tomorrow, it will be difficult to internalize all the ideas and techniques in such a small amount of time.


I really recommend spending some time (when you have time) to learn these techniques; they will prove useful in many strands of math, if not all.

Yes, I am in discrete math now learning truth tables etc. and we will start a fairly brief proof intro soon. That should help, but next fall intro to proof should really help. I just don't know which way to go about these problems. So you struggled solving any problems at all when you started too?

 

[Dick]

I just don't ever recall failing at problems like this. Even when I see solutions to these problems I have a hard time understanding some of them, as does in my estimate other classmates of mine as well; I could be wrong but my guess is they are struggling similar to me.

Sure. But that's no excuse for just emitting gibberish and being angry. Try to read the outline Tsunoyukami posted. It's just using the definitions to draw conclusions. Your earlier comment that "so a int times an int equals an int solved?" is really close to the solution. You just have to put that in a proof context.

 

[Tsunoyukami]

Yes, I am in discrete math now learning truth tables etc. and we will start a fairly brief proof intro soon. That should help, but next fall intro to proof should really help. I just don't know which way to go about these problems. So you struggled solving any problems at all when you started too?

Yes, I struggled solving many problems when starting out. I still struggle solving problems now - sometimes a problem is really easy but you just aren't thinking about it properly; sometimes a problem is hard. There's nothing wrong with encountering a problem that's too difficult for you to solve right away - hopefully, with some hard work and a little bit of controlled frustration and maybe some advice or hints from others you'll figure out a solution - and you'll learn from that problem and maybe the next one will be a little bit easier.

Physics Forums is a great resource with lots of dedicated members who want to help you and want you to succeed and understand the material so if you have a question you should listen to their advice because they're pretty smart and usually give very good hints.


Try to solve this problem following the outline I provided. Write out your solution neatly and precisely; don't skip any steps. Try not to get frustrated if you get stuck - instead, type out what you've done so far - every little bit of information - so we can see where you got stuck and help you better.