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Proving n to be prime Watch

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    hi, not quite sure on how to approach this one in terms of what's an acceptable proof.. help appreciated
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    (Original post by isthislove)
    https://puu.sh/wOHma/af4ffc8c3e.png

    hi, not quite sure on how to approach this one in terms of what's an acceptable proof.. help appreciated
    Can always do it by contradiction (really contraposition though) if you're stuck: assume that n is prime.

    That means you can factorise it into two integers, at least one of which is \leq \sqrt{n}. What does this mean for the prime factors of n?
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    (Original post by isthislove)
    https://puu.sh/wOHma/af4ffc8c3e.png

    hi, not quite sure on how to approach this one in terms of what's an acceptable proof.. help appreciated
    Supposing n is not prime, it must be the product of two integers. One of those must be greater than sqrt(n) in order for the product to be n.
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    (Original post by TheMindGarage)
    Supposing n is not prime, it must be the product of two integers. One of those must be greater than sqrt(n) in order for the product to be n.
    could be square
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    (Original post by Zacken)
    could be square
    Well, the original question said greater than or equal to. If n is the square of a prime, once you check p = sqrt(n), p divides n. If n is the square of a composite number, the first divisor found would be the smallest prime factor of sqrt(n).
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    (Original post by TheMindGarage)
    Well, the original question said greater than or equal to. If n is the square of a prime, once you check p = sqrt(n), p divides n. If n is the square of a composite number, the first divisor found would be the smallest prime factor of sqrt(n).
    yeah but your post didn't, just posting to avoid reader confusion
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    (Original post by isthislove)
    https://puu.sh/wOHma/af4ffc8c3e.png

    hi, not quite sure on how to approach this one in terms of what's an acceptable proof.. help appreciated
    This sort of question makes me glad that I didn't read Maths. In Engineering, you can just state it, as it's obvious
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    (Original post by RogerOxon)
    This sort of question makes me glad that I didn't read Maths. In Engineering, you can just state it, as it's obvious
    This is very elementary, certainly not university level - if you want to be glad you didn't read maths you should see some of the nasty linear algebra I'm trying to understand now...
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    (Original post by IrrationalRoot)
    This is very elementary, certainly not university level - if you want to be glad you didn't read maths you should see some of the nasty linear algebra I'm trying to understand now...
    I prefer the theory to the calculation of 4*4 determinants.
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    (Original post by 13 1 20 8 42)
    I prefer the theory to the calculation of 4*4 determinants.
    I don't. Mindless computation and regurgitation is my bread and butter. Not understanding/creating new things. Course it's not fun though, but neither is struggling with one sentence for half a day and then giving up only to get similarly stuck on the next sentence. Think my mathematical development peaked and stopped in Year 13 lol.
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    (Original post by IrrationalRoot)
    This is very elementary, certainly not university level - if you want to be glad you didn't read maths you should see some of the nasty linear algebra I'm trying to understand now...
    Like I said, it's obvious. I'd find it annoying to write anything other than the conclusion
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    (Original post by RogerOxon)
    Like I said, it's obvious. I'd find it annoying to write anything other than the conclusion
    It is easy to explain vaguely in words, but I think it is non-trivial enough to warrant proving. I am a severe pedant, and a mathematics degree seems to suit me in this regard. Proofs are fun, even if the result is obvious to everyone.

    (Original post by IrrationalRoot)
    I don't. Mindless computation and regurgitation is my bread and butter. Not understanding/creating new things. Course it's not fun though, but neither is struggling with one sentence for half a day and then giving up only to get similarly stuck on the next sentence. Think my mathematical development peaked and stopped in Year 13 lol.
    I am just reeling, months later, from that miserable exam. In general, I do like computation (e.g. Vector Analysis, that was a blast, although admittedly the proofs are even more fun - stuff like Louisville's Theorem, Cauchy's Integral Formula). Algebra I isn't all that bad but I find the notes frustratingly sparse, for so long there was so much I didn't understand, and after filling in a lot of gaps for myself, I wondered why on earth the author hadn't done so himself. I don't think there is anything wrong with your maths skills, it's just that the resources don't facilitate painless comprehension.
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    (Original post by 13 1 20 8 42)
    I am just reeling, months later, from that miserable exam. In general, I do like computation (e.g. Vector Analysis, that was a blast, although admittedly the proofs are even more fun - stuff like Louisville's Theorem, Cauchy's Integral Formula). Algebra I isn't all that bad but I find the notes frustratingly sparse, for so long there was so much I didn't understand, and after filling in a lot of gaps for myself, I wondered why on earth the author hadn't done so himself. I don't think there is anything wrong with your maths skills, it's just that the resources don't facilitate painless comprehension.
    Ok that makes me feel better, I was frustrated at how many things the lecturer left out in these notes and thought that it was only because they were obvious and I was too dumb to understand. That minimal polynomial stuff in particular seems to be plucked out of thin air with no explanation. Doesn't really make sense since it doesn't take much more effort on the author's part to bother to make everything clear and well explained.
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    (Original post by 13 1 20 8 42)
    It is easy to explain vaguely in words, but I think it is non-trivial enough to warrant proving. I am a severe pedant, and a mathematics degree seems to suit me in this regard. Proofs are fun, even if the result is obvious to everyone.



    I am just reeling, months later, from that miserable exam. In general, I do like computation (e.g. Vector Analysis, that was a blast, although admittedly the proofs are even more fun - stuff like Louisville's Theorem, Cauchy's Integral Formula). Algebra I isn't all that bad but I find the notes frustratingly sparse, for so long there was so much I didn't understand, and after filling in a lot of gaps for myself, I wondered why on earth the author hadn't done so himself. I don't think there is anything wrong with your maths skills, it's just that the resources don't facilitate painless comprehension.
    You're making me really regret picking maths for my degree
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    (Original post by Desmos)
    You're making me really regret picking maths for my degree
    Do you not like proofs or...? Rest assured that you do not spend all your time proving the obvious, that tends to come earlier, then you use your skills to tackle more interesting problems.
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    I'm doing a maths degree and tbh I don't understand anything that's been said on this thread. Wish me luck for second year... lol
    But saying that I'm not doing any pure
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    (Original post by 13 1 20 8 42)
    Do you not like proofs or...? Rest assured that you do not spend all your time proving the obvious, that tends to come earlier, then you use your skills to tackle more interesting problems.
    These statements:

    'I am just reeling, months later, from that miserable exam.'

    '...but neither is struggling with one sentence for half a day and then giving up only to get similarly stuck on the next sentence...'

    'I find the notes frustratingly sparse...'
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    (Original post by Desmos)
    These statements:

    'I am just reeling, months later, from that miserable exam.'

    '...but neither is struggling with one sentence for half a day and then giving up only to get similarly stuck on the next sentence...'

    'I find the notes frustratingly sparse...'
    Oh that was just one exam. And really, it was just one question. I didn't even get a bad mark in the exam overall. Most exams were fine, some were even easy.

    Yeah it's module dependent and lecturer dependent I guess. There are some excellent lecturers and some excellent notes, and some not so good lecturers and not so good notes. Plus my experience (and IrrationalRoot's) is just at one uni, I'm sure there's a lot of variation.
 
 
 
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