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3. What is the remainder when 5! 25! Is divided by 31?

3. What is the remainder when 5! 25! Is divided by 31?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Kindly explain in words the problem and solution shown in the picture.

5 = -26 mod (31) -2न mo d (31) 3 = - 28 mod (31) - 29 mod (31) -30 mad (31) If 9 E6 mad (m) and C =d mod (m) then ac E bd mod (m) So, 5.4.3. 2.) = (26)(-27)(-28) (-29)(-30) mod 31 > 5! E(u20)(27)(2s)(29) (30) mad(31) => » 5. 25! =H°(30! mod (31) 125, = 25! mod = 25! mod (31) From wilsons Theorem. pis prime then, (P-1)! = -1 med (P) is prime 31 30! = -1 mod (31) Hence , = fIjo (-+) mod(31) 5,25!
Transcribed Image Text:5 = -26 mod (31) -2न mo d (31) 3 = - 28 mod (31) - 29 mod (31) -30 mad (31) If 9 E6 mad (m) and C =d mod (m) then ac E bd mod (m) So, 5.4.3. 2.) = (26)(-27)(-28) (-29)(-30) mod 31 > 5! E(u20)(27)(2s)(29) (30) mad(31) => » 5. 25! =H°(30! mod (31) 125, = 25! mod = 25! mod (31) From wilsons Theorem. pis prime then, (P-1)! = -1 med (P) is prime 31 30! = -1 mod (31) Hence , = fIjo (-+) mod(31) 5,25!
3. What is the remainder when 5! 25! Is divided by 31?
Transcribed Image Text:3. What is the remainder when 5! 25! Is divided by 31?
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