Let Zsquareroot 2 a b squareroot 2 a b epsilon Z Its not t

Let Z|squareroot 2| = {a + b squareroot 2| a, b epsilon Z}. It\'s not too hard to show (and you don\'t have to) that Z[squareroot 2] is a subring of R. Observe that the element 1 + squareroot 2 is a unit in Z[squareroot 2], because (1 + squareroot 2)(-1 + squareroot 2) = 1 Find ten other units in Z[squareroot 2], not counting 1 + squareroot 2, -1 + squareroot 2, 1, or -1.

Solution

Other units is Z[2] = a+b2 such that a and b are integers are
2+5 (multiply with -2+ 5 and you get = 1)
3+10 (multiply with -3+ 10 and you get=1) and so on for otehr units
4+17
5+26
6+37
7+ 50
8+65
9+82
10+101
and 11+122