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hw6 - (a x 2 3(mod 11 2 23 2(b x 2 9(mod 2 3 3 ...

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Math 465 Problem Set 6 Due Friday, March 21, 2008 1. Evaluate the following Legendre symbols. (Note that 127 is prime.) (a) ( 2 127 ) (b) ( - 1 127 ) (c) ( 11 127 ) (d) ( 15 127 ) 2. How many solutions do the following congruences have? (a) x 2 2 (mod 61) (b) x 2 ≡ - 2 (mod 59) (c) x 2 + 5 x + 1 0 (mod 13) 3. Determine which of the following congruences are solvable.
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Unformatted text preview: (a) x 2 ≡ 3 (mod 11 2 · 23 2 ) (b) x 2 ≡ 9 (mod 2 3 · 3 · 5 2 ) 4. From 7 2 ≡ -1 (mod 5 2 ), find a solution to x 2 ≡ -1 (mod 5 3 ). 5. Evaluate the Jacobi symbol ( 12 35 ) . How many solutions does x 2 ≡ 12 (mod 35) have? 1...
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