Answer the following: 145 mod 20 712 mod 17 Determine whether the following pair of numbers...

Answer the following:
1. 145 mod 20
2. 7¹² mod 17
Determine whether the following pair of numbers are relatively prime. If the answer is not, please give a reason.
1. 34, 11
2. 81, 15
Determine the following
1. GCD(35, 10)
2. GCD(100, 70)

Solutions

Expert Solution

lla 145 = 7X20 +5 .... 145 mod 20 = 5 by 72 = 493-2 (mod.17) 1:5 (72)4 = (-2)" (modif)= 16 (mod 17 ) 9 78 - (mod 17) Now. 78.74 -1.62)? (mod 17) 712 = - 4 (mod 17) 264+17) mod 17) o's 7213 (mod 17) ..:7'? mod 17 = 13 a) Now. ged (34,11)=1. .:. 34,11 are relalively mine by ged (81, 15 ) = 3 +1. therme (81,15) are not relatively mine - bo w 35-10 X3+5 10= 2x5 +0 theregme, ged (35,10)=5 100 = 7071 + 30 70 = 30x2 + 10 30 = 10x3 + 0 os ged (100, 40) = 10

Colby Messinger answered 1 year ago

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