Complex Factors?

Does anyone know of a use for complex factorization in calculating techniques?

Numbers in the form of 2536 can be factored as (50+i6)(50-i6)

Has anyone explored this?

I’m sorry, I don’t have an answer, but I’ve been amazed with all of the recent math posts in this forum lately. How do you guys go about learning how to create and prove all of these mathematical proofs if I may ask? Are there any books or other resources that you’d recommend on the subject? My next semester of college will be filled with proving algorithm efficiencies, so I’d like to familiarize myself with something similar in the mean time.

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The math we are doing is actually fairly basic. Mostly we are just playing with a quadratic expansion but there’s some specialized notation which may make it look difficult. What’s amazing is the speed and accuracy with which some of those guys can execute them.

You must have had some course work in discrete math and calculus? Surely you covered Proof by Induction?

Developing and writing a formal proof is an art which comes with practice and exposure. At first you may feel you don’t know which end to grab a hold of. Learning to read a proof takes some practice too. I’ll see if I can find some articles online.

How to Write a Proof

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Thanks for the resources, there’s a lot to study! I did cover Proof by Induction, but I never used it to test out and write proofs of my own creation.

I will try to find something more concise. You are right. It’s a lot to chew through just to get the general idea.

My two favorite proof schemes are

Proof by Induction: Here you never actually do the proof for each case, you just threaten to if challenged.

Proof by Contradiction Here you start off with what you believe to be a false assumption and prove a true statement.

Here’s a simple exercise,if you like. Do a formal proof that there is no largest integer. It’s trivial but a lot of people flounder with that.

There is some fun to be had. There is a proof from Medieval times that demonstrates how, if you accept a contradiction as true you can prove anything. Betrand Russell once used this trick to prove to an audience that he was the Pope. :slight_smile:

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It is an interesting idea. However; I currently see no use in this.
On the other hand; I don’t want to dismiss it either.

My thoughts the same.