ws8 - x 3 (mod 4) x 2 (mod 5) x 5 (mod 7) 4. Suppose we...

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Rob Bayer Math 55 Worksheet July 7, 2009 Instructions Introduce yourselves! Despite popular belief, math is in fact a team sport! Find some blackboard space, a piece of chalk, and decide who will be your first scribe. Do the problems below, having a different person be the scribe for each one. Try to work out the problems as a group, but feel free to flag me down if you run into a wall. Linear Congruences and the CRT 1. Find an inverse of 9 mod 20. 2. Solve the congruence 6 x 15 (mod 21) 3. Solve the system of congruences
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Unformatted text preview: x 3 (mod 4) x 2 (mod 5) x 5 (mod 7) 4. Suppose we want to nd 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 vice-versa. (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 nd all solutions to x 2 4 (mod 35) 5. Compute 7 130 mod 11. Hint: this requires 1-2 lines of work....
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