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Number Theory – Winter 2015

January 17, 2015

The problem statement: Find all the integer solutions of x2+2y2=1.

Some pairs of number (could be positive or negative)

x y
1 0
3 2
17 12
99 70

Conjectures:

1) y is even, x is odd: proof was given

2) Solutions get farther and farther apart

3) The sum of two consecutive y’s  = the difference of two consecutive x’s

Need to know how to solve quadratic equation.  One knows and is sharing the derivation.

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