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Age 16 to 18 Challenge Level:

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 $p$?