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# Could someone explain this please watch

1. I have in my notes:

a divides y, b divides y, gcd(a,b) = 1 thus ab divides y.

Can someone explain this to me.

Thanks
2. Suppose and . Then since , we have that each of the are distinct (for all i,j). If then and if then (for some constant integers ), but because of unique prime factorisation we must have (for some constant integer ), and hence (for some constant integer , and hence .

This is a bit messy and there's probably a neater way of showing it than this, but you get the idea.

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Updated: January 21, 2010
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