Find all the integers x which are the solutions to the following congruences.
x^2 is equivalent to 2 mod 17
Find all the integers x which are the solutions to the following congruences. x^2 is equivalent...
Find all integers x, y, 0 < x, y < n, that satisfy each of the following pairs of congruences. If no solutions exist, explain why. (a) x + 5y = 3(mod n), and 4x + y = 1(mod n), for n = 8. (b) 7x + 2y = 3(mod n), and 9x + 4y = 6(mod n), for n=5.
Find all solutions to the following linear congruences. (15 points) (a) 2x ≡ 5 (mod 7). (b) 6x ≡ 5 (mod 8). (c) 19x ≡ 30 (mod 40). Show all the steps taken in neat English to receive a positive review
Let Xe be the set of integers x which satisfy the system of congruences 42 mod 3121, 7 mod 11, c od 2019 What is the smallest integer in the set
Let Xe be the set of integers x which satisfy the system of congruences 42 mod 3121, 7 mod 11, c od 2019 What is the smallest integer in the set
2. For each of the following, find all integers a with 0 S < n, satisfying the following congruences modulo n. (a) 3x5 (mod 7) (b) 3x 5(mod 6) (c) 3x 3(mod 7) (d) 3 3 (mod 6) (e) 2x 3(mod 50) (f) 22r 15(mod 67) (g) 79x 12 (mod 523)
2. For each of the following, find all integers a with 0 S
How many classes of solutions are there for each of the following congruences? (a) x2 - 1 = 0 mod (168) (b) x2 + 1 = 0 mod (70) (c) x2 + x + 1 = 0 mod (91) (d) x3 + 1 = 0 mod (140) Please note to show how you got the solutions as well as finding out how many classes of solutions there are for each congruence. Please explain every step so I can understand how...
find all integers such that (x^86) is equivalent to (6 mod 29) . plese explain each step in detail
7) Determine if the following congruences have solution(s) and find the solutions if they exist: a. 22x = 4 mob 29 b. 51x = 21 mob 36 C. 35x = 15 mod 182 d. 131x = 21 mob 77 e. 20x = 16 mob 64
Find all solutions of the congruences:
(e) 64x 83 (mod 105) (f) 589x 209 (mod 817) (g) 49x 5000 (mod 999)
(e) 64x 83 (mod 105) (f) 589x 209 (mod 817) (g) 49x 5000 (mod 999)
A) If possible, solve the following system of congruences using either of the two methods of this section. x ≡ 4 (mod 11) x ≡ 3 (mod 17) x ≡ 6 (mod 18) B) Find the inverse of 19 modulo 23. Show all steps taken in neat English to receive a positive review
Arrange the steps in the correct order to solve the system of congruences x 2 (mod 3), x 1 mod 4). and x3 (mod 5) using the method of back substitution Rank the options below Thus, x= 31.2 - 3/4 + 1)2 - 120+5 We substitute this into the third congruence to obtain 12.5 13 mod 5), which implesu li imod 5) Hence, w5v4 and so x 12.5 - 12/5 + 4) - 5 - 60v. 53, where vis an...