# Prove if x^2 is divisible by a prime p then so is x

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I am trying to use the contrapositive by proving if x is NOT divisible by p then neither is x^2.

But I don't know how to it for a general prime p?

But I don't know how to it for a general prime p?

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#2

(Original post by

I am trying to use the contrapositive by proving if x is NOT divisible by p then neither is x^2.

But I don't know how to it for a general prime p?

**lightningdoritos**)I am trying to use the contrapositive by proving if x is NOT divisible by p then neither is x^2.

But I don't know how to it for a general prime p?

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#5

(Original post by

I'd like to try both but I'm more used to using euclids lemma

**lightningdoritos**)I'd like to try both but I'm more used to using euclids lemma

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#6

You can also use strong induction to prove the fundamental theorem of arithmetic. If you wanna be really safe, first use the Well Ordering Principle to prove the Principle of Induction.

(Original post by

I'd like to try both but I'm more used to using euclids lemma

**lightningdoritos**)I'd like to try both but I'm more used to using euclids lemma

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#7

(Original post by

You can also use strong induction to prove the fundamental theorem of arithmetic. If you wanna be really safe, first use the Well Ordering Principle to prove the Principle of Induction.

**13 1 20 8 42**)You can also use strong induction to prove the fundamental theorem of arithmetic. If you wanna be really safe, first use the Well Ordering Principle to prove the Principle of Induction.

Have you been revising too much number theory?

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#8

I have indeed, which isn't good because I should be studying the much trickier sets and countability stuff lol

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#9

(Original post by

I have indeed, which isn't good because I should be studying the much trickier sets and countability stuff lol

**13 1 20 8 42**)I have indeed, which isn't good because I should be studying the much trickier sets and countability stuff lol

What twisted things are in the course?

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#10

Didn't we have a question very similar to this a few weeks ago?

I believe the solution related to prime factors.

I believe the solution related to prime factors.

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#11

(Original post by

Ooh, those are much more fun than number theory, although, to be fair - I've only done the really basic stuff, cardinal numbers, bijections between this set and that, aleph-naught, etc...

What twisted things are in the course?

**Zacken**)Ooh, those are much more fun than number theory, although, to be fair - I've only done the really basic stuff, cardinal numbers, bijections between this set and that, aleph-naught, etc...

What twisted things are in the course?

edit: well the proof given is more long and unsatisfying than convoluted

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#12

(Original post by

The stuff is mostly that basic but the past paper questions are not lol, probably because I missed lectures and the notes leave the actually difficult stuff as exercises without solutions. It ties it into the function theory a lot, using injections and inverses and all that in the proofs; there's also power sets, a little bit on transcendental vs algebraic numbers, unions of countable sets; there's the Schroeder-Bernstein Theorem, which I hope they do not ask us to name, and its convoluted proof.

edit: well the proof given is more long and unsatisfying than convoluted

**13 1 20 8 42**)The stuff is mostly that basic but the past paper questions are not lol, probably because I missed lectures and the notes leave the actually difficult stuff as exercises without solutions. It ties it into the function theory a lot, using injections and inverses and all that in the proofs; there's also power sets, a little bit on transcendental vs algebraic numbers, unions of countable sets; there's the Schroeder-Bernstein Theorem, which I hope they do not ask us to name, and its convoluted proof.

edit: well the proof given is more long and unsatisfying than convoluted

How many lectures do you miss?

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#13

(Original post by

This is first term Warwick stuff? Impressive. :-)

How many lectures do you miss?

**Zacken**)This is first term Warwick stuff? Impressive. :-)

How many lectures do you miss?

To be fair I was very consistent, apart from the super boring physics module I ended up dropping, until maybe the last week when I missed practically everything. Oh and a fair few differential equations ones before that because I lost the will to live trying to follow those lectures...

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#14

note p|x^2 <-> p^2|x^2

Note in a square each prime factor occurs an even number of times hence atleast divisble by p^2.

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Note in a square each prime factor occurs an even number of times hence atleast divisble by p^2.

Posted from TSR Mobile

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