Number Theory | Fundamental Theorem of Arithmetic

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We give a proof of the Fundamental Theorem of Arithmetic.

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This is one of the best explanations of the FTA that I have ever seen. If there is any way, it should be broadcast on prime-time!

PunmasterSTP

Loved the proof, really big help for my number theory course!

jacobbarats

Professor Penn, thank you for a well explained mathematical proof of The Fundamental Theorem of Arithmetic.

georgesadler

Not seen the pbc method on this one before. Good one.

without

Think how Euclid did this proof without algebra 2300 years ago.

jhumasarkar

Can you write in a product of powers of primes?

RGAstrofotografia

Shoutout to the green(screen) on the T-shirt

achrafBadiry

Why do I feel that the beginning of the proof is sick?! When you believe that numbers are either prime or composite and you use this fact, there would be nothing left to prove except uniqueness.

erfanmohagheghian

Hmmm, how are a, b guaranteed to exist? What if the smallest natural number for which the unique factorization didn't exist was 1? Then there are no natural numbers strictly between 1 and 1. And 1 is not prime (and not composite). But of course 1 has a unique prime factorization where all the powers are zero, so with our assumption the min of the set of natural numbers not in the form must be greater than 1, but I think that consideration has to be made.

moshadj

I do not understand the statement: "Observe that m must be composite, otherwise it is already in the form." The form itself is a composite of primes. If m is the smallest integer without the form equivalent to a product of primes to natural powers, why does that mean it has to be composite???
A form not equivalent to the representation is one of the form as given, plus or minus one... aka

m = p_1^e_1 ... p_n^e_n + 1 (or minus 1).

Seems like to me you would have to do "proof by induction" with "proof by contradiction" on the form above. Sorry, not convinced by the proof as given unless you can explain better this composite business MP. Fair thee well.

paulkohl

I love the continents on your shirt! Ha!

williamdirks

Lol. Was more focused on his muscles than the proof.
Then I noticed the crag of Ceuse in the background. This dude climbs pretty hard probably

JTurfie

Nice But looking from other device not shown in screeen 😂😂😂😂😂

abuabdullaahiwaaaishatah

if one prime divides the other, they do not have to be the same.

michaelempeigne

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