Given p > 2 a prime number, prove that: (p+1 |("") = 0(modp 5.1) for any natural number 2 snsp-1 ) = (-1)" (mod p) 5.2) for any 0snsp- 1,EN = 2 (mod p). 5.3) [fuggontion: lco E 1 ond E ah

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 30E: 30. Prove that any positive integer is congruent to its units digit modulo .
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5)
Given p > 2 a prime number, prove that:
p+1)
= 0 (mod p)
5.1)
for any natural number 2 snsp-1
= (-1)" (mod p)
5.2)
| for any 0snsp– 1, €N
= 2 (mod p).
5.3)
[Suggestion: Use 5.1 and 5.2]
Transcribed Image Text:5) Given p > 2 a prime number, prove that: p+1) = 0 (mod p) 5.1) for any natural number 2 snsp-1 = (-1)" (mod p) 5.2) | for any 0snsp– 1, €N = 2 (mod p). 5.3) [Suggestion: Use 5.1 and 5.2]
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