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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 $p$?