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HOMEWORK XI
MATH-UA 0248-001 THEORY OF NUMBERS due on Dec, 8, 2017
1. Determine the infinite continued fraction representation of √ 26.
2. Establish that if x0, y0 is a solution of the equation x2 −dy2 = −1, then x= 2x20+ 1, y = 2x0y0 satisfiesx2−dy2 = 1.
3. Ifdis divisible by a primep≡3(mod4), show that the equationx2−dy2 =−1 has no solution.
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