Unformatted text preview: x ≡ 3 (mod 4) x ≡ 2 (mod 5) x ≡ 5 (mod 7) 4. Suppose we want to ﬁnd all solutions to x 2 ≡ 4 (mod 35) (a) Explain why any such solution must also be a solution to the system ( x 2 ≡ 4 (mod 5) x 2 ≡ 4 (mod 7) and viceversa. (b) Solve each of the congruences in (a) individually to show that x ≡ 2 or 3 (mod 5) and that x ≡ 2 or 5 (mod 7) (c) Use the CRT on each of the possibilities from (b) to ﬁnd all solutions to x 2 ≡ 4 (mod 35) 5. Compute 7 130 mod 11. Hint: this requires 12 lines of work....
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 Summer '08
 STRAIN
 Math, Congruence relation, Linear Congruences, Rob Bayer, blackboard space

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