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# uni maths problem watch

1. i needed some help with this question:
let n belong to N (natural numbers) and a1, a2, ......, ak belong to Z (intergers). Show that if (n, ai)=1 for all i, then (n, a1a2a3....ak)=1, where (n, ai)=1 means the greatest common divisor of n and ai is 1.
2. Suppose the prime p divides (n, a_1*a_2*...*a_k). Then p divides n and p divides a_1*...*a_k, so...
3. You can interpret to mean " does not share any prime factors with any ". Since prime factorisation is unique, the result follows after a few lines of working.
4. This is a university problem?
Well implies . So what about the product ?

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Updated: January 24, 2010
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