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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.

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    Maybe you could specify more clearly what it is exactly that you would like to prove?2012-08-31
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    i prove already that if c is prime and divides ab then c divides a or b2012-08-31
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    And what is the generalization that you wish to prove?2012-08-31
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    i 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 nice2012-08-31
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    my idea is using induction Euclid lemma will be a starting point for n=2 my property is true2012-08-31
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    now i have to go suppose at the rank n and show the that the property is true at the rank n+12012-08-31
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    like if c divides a1.....an then its divides ai and prove that is true for a1.....an.an+12012-08-31
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    normally 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 luck2012-08-31

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