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1.21. Let m € Z. (a) Suppose that m is odd. What integer between 1 and m - 1 equals 2-¹ mod m? (b) More generally, suppose that m = 1 (mod b). What integer between 1 and m - 1 is equal to b¹ mod m?

1.21. Let m € Z. (a) Suppose that m is odd. What integer between 1 and m - 1 equals 2-¹ mod m? (b) More generally, suppose that m = 1 (mod b). What integer between 1 and m - 1 is equal to b¹ mod m?

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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**1.21.** Let \( m \in \mathbb{Z} \). (a) Suppose that \( m \) is odd. What integer between 1 and \( m - 1 \) equals \( 2^{-1} \) mod \( m \)? (b) More generally, suppose that \( m \equiv 1 \ (\text{mod} \ b) \). What integer between 1 and \( m - 1 \) is equal to \( b^{-1} \) mod \( m \)?
Transcribed Image Text:**1.21.** Let \( m \in \mathbb{Z} \). (a) Suppose that \( m \) is odd. What integer between 1 and \( m - 1 \) equals \( 2^{-1} \) mod \( m \)? (b) More generally, suppose that \( m \equiv 1 \ (\text{mod} \ b) \). What integer between 1 and \( m - 1 \) is equal to \( b^{-1} \) mod \( m \)?
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