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'Binaring' printed from http://nrich.maths.org/
Consider $(1 + \sqrt2)^n$. This will be of the form $A + B\sqrt2$
where $A$ and $B$ are integers. Decide which entries in the table
below are possibe and which are not.

A even 
A odd 
B even 


B odd 


What happens for $(a + \sqrt p)^n$ for other values of $p$?