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HOMEWORK 10
MATH-UA 0248-001 THEORY OF NUMBERS due on Dec, 7, 2020
1. Determine the infinite continued fraction representation of √ 26.
2. Find a solution of the equation x2−41y2 = 1. (Hint: √
41 = [6,2,2,12].) 3. Establish that if x0, y0 is a solution of the equation x2 −dy2 = −1, then
x= 2x20+ 1, y = 2x0y0 satisfiesx2−dy2 = 1.
4. Ifdis divisible by a primep≡3(mod4), show that the equationx2−dy2 =−1 has no solution.
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