Find x in the following questions
1. 3072757632 mod x = 0 (where x>= 5907)
Find x in the following questions 1. 3072757632 mod x = 0 (where x>= 5907)
(0. 0), (0.2), and e2an model for uclidean geometry. Find the images of the points (0, 0), (0,2), and (2, 1) under the following isometries. ssume the Cartesian mod 1. A (a) The reflection across the line with equation x y. (b) The reflection across the line x y 5. (c) The half-turn about (-1, 1). (d) The rotation through 45e in the counterclockwise direction about the point (2,2). (e) The glide reflection GAB, where A (-2.0) and B (0.1)...
9. Use the construction in the proof of the Chinese remainder theorem to find a solution to the system of congruences X 1 mod 2 x 2 mod 3 x 3 mod 5 x 4 mod 11 10. Use Fermats little theorem to find 712 mod 13 11. What sequence of pseudorandom numbers is generated using the linear congruential generator Xn+1 (4xn + 1) mod 7 with seed xo 3?
9. Use the construction in the proof of the Chinese...
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 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.
2. Use modular arithmetic rules to find out the following: Use the rule: (a*b) mod x -( (a mod x) (b mod x)) modx Find out: (97)49 mod 119 Hints: 49 can be written as: 49-32 16+1 Try finding out 97 mod 119 Then, 972 mod 119, then 974 mod 119 etc.
Please solve the above 4 questions.
1. Using the extended Euclidean Algorithm, find all solutions of the linear congruence 217x 133 (mod 329), where 0 x < 329 (Eg. if 5n, n 0,. ,6) 24 + 5n, п %3D 0, 1, . .., 6, type 24 + x< 11 2. Find all solutions of the congruence 7x = 5 (mod 11) where 0 (Eg. if 4,7 10, 13, type 4,7,10,13, none. or if there are no solutions, type I 3....
Find all solutions to the congruence x2+ x+ 1≡0 mod 91. (Hint:factor the modulus, use trial and error to find the solutions modulo the factors, and the CRT to combine the results into solutions to the original equations.)
x(0)=1, x'O)= 0, where f(t) = 1 if t< 2; and f(t) = 0 if Find the solution of X"' + 2x' + x=f(t), t> 2.
1. Show that the number of solutions (x mod p, y mod p) to the equation x² + 1 = y2 mod p is p- p (6+1) k=0
Find:
1. Find (2x2 + y2) DV where Q = { (x,y,z) 0 < x <3, -2 <y <1, 152<2} ЛАЛ