find all integers such that (x^86) is equivalent to (6 mod 29) .
plese explain each step in detail
find all integers such that (x^86) is equivalent to (6 mod 29) . plese explain each...
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 the integers x which are the solutions to the following congruences. x^2 is equivalent to 2 mod 17
find all integers x that are solution for 4x modullo 1 (mod 5)
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
Problem 1 Use the Chinese remainder theorem, find all integers x such that: (20 pts) x = 1 (mod 5) x = 2 (mod 7) x = 3 (mod 9) x = 4 (mod 11)
Problem 1 Use the Chinese remainder theorem, find all integers x such that: (20 pts) x = 1 (mod 5) r = 2 (mod 7) x = 3 (mod 9) I= 4 mod 11) Answer,
Question 13 (0.5 points) For all positive integers a and b, if al0 = 1 (mod b) then a = 1 (mod b). True False Question 14 (0.5 points) For all positive integers an, az, mi and m2, if mı #m2 then the system of linear congru- ences x =ai (mod mi) x = a2 (mod m2) admits at most one solution modulo mim2. True O False Question 15 (0.5 points) For all positive integers a and b, if a|b2...
Please explain each step in the solution
6. Find the equivalent capacitance of the combination. Assume that Ci is 10 uF, C2 is 5uF and C3 is 4uF (2 marks)
Plese solve the step by step my teacher wants all step.
Exercise 1 (10 pts) {x?in(x)dx
1. Solve each linear congruence for all integers x so that 0 sx <m a) 11x 8 (mod 57) b) 14x 3 (mod 231)