4P- Problem 7. Show that for each prime p 2 5, the integer m, = " is a pseudoprime to base 2. Problem 8. Suppose 1 has a non-trivial square root modulo m (i.e. x² = 1 (mod m) but x ±1 (mod m)), then 1< gcd(x±1, m) < m.
4P- Problem 7. Show that for each prime p 2 5, the integer m, = " is a pseudoprime to base 2. Problem 8. Suppose 1 has a non-trivial square root modulo m (i.e. x² = 1 (mod m) but x ±1 (mod m)), then 1< gcd(x±1, m) < m.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
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if possible both questions plz
Transcribed Image Text:4P-1
Problem 7. Show that for each prime p 2 5, the integer m, = is a pseudoprime to base 2.
Problem 8. Suppose 1 has a non-trivial square root modulo m (i.e. x² = 1 (mod m) but x +1
(mod m), then 1< gcd(x±1, m)< m.
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