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Let n = pq, where p and q are distinct primes such that p = q = 3 (mod 4). Suppose a E Z+ with a < n. Prove that if the Jacobi symbol (a/n) = 1, then a ^[p(n)/4] = ±1 (mod n).

Let n = pq, where p and q are distinct primes such that p = q = 3 (mod 4). Suppose a E Z+ with a < n. Prove that if the Jacobi symbol (a/n) = 1, then a ^[p(n)/4] = ±1 (mod n).

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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Let n = pq, where p and q are distinct primes such that p = q = 3 (mod 4). Suppose a E Z+ with a <n. Prove that if the Jacobi symbol (a/n) = 1, then a ^[p(n)/4] = ±1 (mod n).
Transcribed Image Text:Let n = pq, where p and q are distinct primes such that p = q = 3 (mod 4). Suppose a E Z+ with a <n. Prove that if the Jacobi symbol (a/n) = 1, then a ^[p(n)/4] = ±1 (mod n).
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