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(a) It is a fact that 14 is a primitive root mod 29 and that 1428 = 1 mod 29². Use this information to find a primitive root mod 29². (b) Let m = 29¹0. Use your answer to part (a) to find an integer b coprime to m such that ordm (b) = 7.29⁹.

(a) It is a fact that 14 is a primitive root mod 29 and that 1428 = 1 mod 29². Use this information to find a primitive root mod 29². (b) Let m = 29¹0. Use your answer to part (a) to find an integer b coprime to m such that ordm (b) = 7.29⁹.

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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(a) It is a fact that 14 is a primitive root mod 29 and that 1428 = 1 mod 29². Use this information to find a primitive root mod 29². (b) Let m = 29¹0. Use your answer to part (a) to find an integer b coprime to m such that ordm (b) = 7.29⁹.
Transcribed Image Text:(a) It is a fact that 14 is a primitive root mod 29 and that 1428 = 1 mod 29². Use this information to find a primitive root mod 29². (b) Let m = 29¹0. Use your answer to part (a) to find an integer b coprime to m such that ordm (b) = 7.29⁹.
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