(1 point) Find the smallest positive integer solution to the following system of congruence: x =...
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),
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
let m=(82! /21). find the smallest positive integer x such that m≡x(mod 83)
Modern Algebra, MAT 401 Test 3. Show your work (b) 1. Find a solution x E ZOSXsn for the congruence (a) 8x+3= 5 mod 9 8x=l(mod 21) 2. Find the least positive integer that is congruent to: (a) (14+46+65+92Xmod 11) (b) (717)(32)(62)(mods) (c) 62(mod5) 3. Solve the system (a) x = 2(mod 5) em a lx = 3(mod 8) x 4(mod 7) (3x + 2 = 3(mod 8) 4. Solve the system (a) [4][x] + [2][y] = [1] () {[3][x]...
8-7. Find the smallest positive integer a such that 5:13 +13n" + a(9) = 0 (mod 65) for all integers n.
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
the integer x such that 5 3 (mod 7) 57 (mod 61) e linear congruence 31
Solve the following system of equations and find all congruence class solutions if any exist; if no solution exists, explain why not: x24 (mod 35) 3.x 15 mod 21)
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...
5. (20 points) Solve the system of congruences x (mod 13) and 11 (mod 24). Find the smallest nonnegative integer solution to the system.