Kindly explain in words the problem and solution shown in the picture. 5 = -26 mod (31)-2न mo d (31)3 = - 28 mod (31)- 29mod (31)-30 mad (31)If9 E6 mad (m) andC =d mod (m)thenac 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. pisprime then,(P-1)! = -1 med (P)is prime3130! = -1 mod (31)Hence ,= fIjo (-+) mod(31)5,25! 3. What is the remainder when 5! 25! Is divided by 31?

Given: 5!25!31 To find: Remainder

Answered: 3. What is the remainder when 5! 25! Is…

Math

Calculus

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

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter11: Rational And Irrational Numbers

Section11.8: Adding And Subtracting Radicals

Problem 3E

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Question

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!

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

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