Find the smallest positive inverse of 10 (mod 17)
10* 0 % 17 = 0 10* 1 % 17 = 10 10* 2 % 17 = 3 10* 3 % 17 = 13 10* 4 % 17 = 6 10* 5 % 17 = 16 10* 6 % 17 = 9 10* 7 % 17 = 2 10* 8 % 17 = 12 10* 9 % 17 = 5 10* 10 % 17 = 15 10* 11 % 17 = 8 10* 12 % 17 = 1 So, the answer is 12
12
Find the smallest positive solution and the general solution to the system x ≡ 1 (mod 3), x ≡ 2 (mod 5) and x ≡ 3 (mod 7). Exercise 2 (5 points Find the smallest positive solution and the general solution to the system ΧΞ2 (mod 5) and r Ξ 3 (mod 7). 1 (mod 3),
Find the additive inverse of the following value mod m. 16. 7 mod 9 17. 4 mod 12 18. 63 mod 30 19. 222 mod 3
Find the biggest negative and smallest positive inverses of 13 (mod 21).
8-7. Find the smallest positive integer a such that 5:13 +13n" + a(9) = 0 (mod 65) for all integers n.
let m=(82! /21). find the smallest positive integer x such that m≡x(mod 83)
1. (a) Use the Extended Euclidean Algorithmn to compute the inverse of 10 mod 17. (b) Use your answer from (a) so solve the equation 10x = 8 mod 17. (c) Compute 1616 mod 17. You may assume that Fermat’s Little Theorem is true.
What is the smallest positive integer n that has the following characteristics? n mod 3=2,n mod 5=3, and n mod 7=5
Please answer the following two questions. Find the smallest positive integer solution to the equation. Show all of your work. x = 4 mod 7 Find the smallest positive integer solution to the equation. Show all of your work. x5 = 11 mod 35
(1 point) Find the smallest positive integer solution to the following system of congruence: x = 5 (mod 19) = 2 (mod 5) = 7 (mod 11) x =
Using the Extended Euclidean Algorithm, find the multiplicative inverse of: 31 mod 3480