Friday, 15 April 2016

number theory - Given a+sqrtb with positive integer a,b, find a and b?

Suppose I had n=a+b as a decimal of arbitrary precision, but didn't know a or b, except that they are positive integers.




If I had just b, I could just square it and end up with something very close to an integer, so I'd have b.



If I take n22an, I get (a2+b+2ab)(2a2+2ab)=ba2 which will be an integer, but I don't have a...



Is there some way to take the sum of the integral and decimal portion of n and do some integer voodoo there?



Thanks for any ideas.

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