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  3. question 2 in this question youll prove the following statement...

Question: question 2 in this question youll prove the following statement...

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Question 2. In this question you'll prove the following statement about prime numbers:Question 2. In this question youll prove the following statement about prime1 numbers: Vn EN, 3m ENs.t. mn and m is prime. You may find it useful to recall the following standard thcorem. Theorem. For all a, b EN here erist a unique quotient q and remainder r in Z+ such thal we have both a qb + r and 0 r<q. a) Write down, in formal notation, the negation of the statement (t). b) Give a one sentence informal version of your formal statement in part a) c) Prove that if n1, n2, ,nk EN are each at least 2 then n nk1 is not divisible by any of the numbers ni,n2,..,n d) Prove that the truth of the statement in part a) leads to a contradiction, and hence that (t) must be true. [Hint: use your theorems (and we havent proved many!).]

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