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Use this theorem to solve the following congruences: (1) x° = 2 mod 35 (2) x' = 13 mod 35

Use this theorem to solve the following congruences: (1) x° = 2 mod 35 (2) x' = 13 mod 35

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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Use this theorem to solve the following congruences: (1) x° = 2 mod 35 (2) x1! = 13 mod 35
Transcribed Image Text:Use this theorem to solve the following congruences: (1) x° = 2 mod 35 (2) x1! = 13 mod 35
Theorem. If gcd(e, o(m)) = 1, then for any a e (Z/mZ)*, х 3 а mod m has a unique solution given by x = ad where d is the multiplicative inverse for e modulo o(m).
Transcribed Image Text:Theorem. If gcd(e, o(m)) = 1, then for any a e (Z/mZ)*, х 3 а mod m has a unique solution given by x = ad where d is the multiplicative inverse for e modulo o(m).
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