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Suppose we want to compute x = a (mod pq) for primes p and q, utilizing the Chinese Remainder Theorem and Fermat's Little Theorem. Select the true statements. The Chinese Remainder Theorem guarantees a unique solution to any system of modular equations. 1 Fermat's Little Theorem allows us to conclude that a²-¹ = 1 (mod p) for any integer a and any prime p. By CRT, x = (a¹ mod p) (q-¹ mod p)q + (a¹ mod p) (p-¹ mod q)p

Suppose we want to compute x = a (mod pq) for primes p and q, utilizing the Chinese Remainder Theorem and Fermat's Little Theorem. Select the true statements. The Chinese Remainder Theorem guarantees a unique solution to any system of modular equations. 1 Fermat's Little Theorem allows us to conclude that a²-¹ = 1 (mod p) for any integer a and any prime p. By CRT, x = (a¹ mod p) (q-¹ mod p)q + (a¹ mod p) (p-¹ mod q)p

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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Suppose we want to compute x = a (mod pq) for primes p and q, utilizing the Chinese Remainder Theorem and Fermat's Little Theorem. Select the true statements. The Chinese Remainder Theorem guarantees a unique solution to any system of modular equations. 0-1 Fermat's Little Theorem allows us to conclude that a²-¹ = 1 (mod p) for any integer a and any prime p. By CRT, x = (ab mod p) (q-¹ mod p)q + (a' mod p) (p-¹ mod q)p 1 By CRT, x = (a' mod q) (q-¹ mod p)q + (a' mod q) (p¯¹ mod q)p If b ≥ p, then ab-p+1 = ab (mod p). If b = c (mod p), then a³ = aº (mod p).
Transcribed Image Text:Suppose we want to compute x = a (mod pq) for primes p and q, utilizing the Chinese Remainder Theorem and Fermat's Little Theorem. Select the true statements. The Chinese Remainder Theorem guarantees a unique solution to any system of modular equations. 0-1 Fermat's Little Theorem allows us to conclude that a²-¹ = 1 (mod p) for any integer a and any prime p. By CRT, x = (ab mod p) (q-¹ mod p)q + (a' mod p) (p-¹ mod q)p 1 By CRT, x = (a' mod q) (q-¹ mod p)q + (a' mod q) (p¯¹ mod q)p If b ≥ p, then ab-p+1 = ab (mod p). If b = c (mod p), then a³ = aº (mod p).
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