1. Prove (a,b)=1 iff (a+b, ab)=1(adsbygoogle = window.adsbygoogle || []).push({});

I'm guessing the main tools I have here are xa+yb=1 and the lemma behind the Euclidean algorithm: if a=bq+r, (a,b)=(b,r). I figure I need to do lots of manipulation to build up a more complicated equality, but I can't make it quite work. Any suggestions?

2. Suppose x an integer such that 0<x<n^3. Show there exist a_0, a_1, a_2 in {0,1,...,n-1} such that x=a_0+a_1n+a_2n^2

I don't even know where to start this one.

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# Number theory questions

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