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You and your friend Lara are considering the linear congruence ax = b (mod m), where m = 6 x 11 x 233, b = 232 x 379 and a is an unspecified integer in the range 2645 < a < 2665. In this question you may assume that 11, 23 and 379 are prime numbers, and you may use the table of prime factorisations given at the bottom of the question. (a) Lara askes you to give all a in the range 2645

You and your friend Lara are considering the linear congruence ax = b (mod m), where m = 6 x 11 x 233, b = 232 x 379 and a is an unspecified integer in the range 2645 < a < 2665. In this question you may assume that 11, 23 and 379 are prime numbers, and you may use the table of prime factorisations given at the bottom of the question. (a) Lara askes you to give all a in the range 2645

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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You and your friend Lara are considering the linear congruence ax = b (mod m), where m = 6 x 11 x 233, b = 232 x 379 and a is an unspecified integer in the range 2645 < a < 2665. In this question you may assume that 11, 23 and 379 are prime numbers, and you may use the table of prime factorisations given at the bottom of the question. (a) Lara askes you to give all a in the range 2645 < a < 2665 for which the linear congruence ax = b (mod m) has a unique solution modulo m. Enter your answer in the box below and make sure you follow the syntax advice. Answer: the linear congruence has a unique solution for a in the set
Transcribed Image Text:You and your friend Lara are considering the linear congruence ax = b (mod m), where m = 6 x 11 x 233, b = 232 x 379 and a is an unspecified integer in the range 2645 < a < 2665. In this question you may assume that 11, 23 and 379 are prime numbers, and you may use the table of prime factorisations given at the bottom of the question. (a) Lara askes you to give all a in the range 2645 < a < 2665 for which the linear congruence ax = b (mod m) has a unique solution modulo m. Enter your answer in the box below and make sure you follow the syntax advice. Answer: the linear congruence has a unique solution for a in the set
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