How to prove a generalized Euclid lemma par induction after proving Euclid lemma?
I want to prove the generalized lemma, to prove by rearranging the product of number and use Euclid lemma as a model. A proof will be nicer if it can use induction principle.
Euclid lemma by induction
3
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elementary-number-theory
induction
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0Maybe you could specify more clearly what it is exactly that you would like to prove? – 2012-08-31
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0i prove already that if c is prime and divides ab then c divides a or b – 2012-08-31
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0And what is the generalization that you wish to prove? – 2012-08-31
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0i want to prove that if c is prime and divides any product of number then it divides a least one of the member of the product but i want to use induction, i did without induction but its no really nice – 2012-08-31
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0my idea is using induction Euclid lemma will be a starting point for n=2 my property is true – 2012-08-31
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0now i have to go suppose at the rank n and show the that the property is true at the rank n+1 – 2012-08-31
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0like if c divides a1.....an then its divides ai and prove that is true for a1.....an.an+1 – 2012-08-31
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1normally i edit one giant sentence posts which have 47 words your sentence is such a shocking example so i think i will leave it as is everyone can then see why it is kind of hard to read we hopefully will encourage the use of punctuation that way dont you agree i may as well use at least one punctuation mark, there we go now we have an awesome comma splice to fill out my comment i voted for your post as penance for using your question as a punching bag good luck – 2012-08-31