Mathematics

Mathematics, 10.07.2019 03:10, litwork1726

Either find a solution x ? z for the following congruence equations, or show that no solution exists.
(a)99x ? 18 mod30, (b) 91x ? 84 mod 143.

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Mathematics, 12.07.2019 19:20, bluetopaz447

(c) show that if p is any polynomial with integer coefficients, and if a = b (mod m), then p(a) = p(b) (mod m). 6. let me n, and a, b e z. consider the problem of solving the follow- ing congruence ar = b (mod m). a solution is any number k for which ak – b is divisible by m. (a) show that 7 is a solution of the congruence 4x = 3 (mod 5). find all other solutions of this congruence. (b) find all solutons of the congruences (i) 4x = 3 (mod 6) (ii) 4x = 2 (mod 6). (c) let g = gcd(a,m). show that, if ar = b (mod m) has a solution, then g|b. (d) conversely, show that if a gcdlem) and alh then the con-

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Mathematics, 14.07.2019 16:00, EricaCox1

Asystem of equations is shown below: x + 3y = 5 (equation 1) 7x − 8y = 6 (equation 2) a student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. if equation 2 is multiplied by 1, which of the following steps should the student use for the proof? show that the solution to the system of equations 3x + y = 5 and 8x −7y = 6 is the same as the solution to the given system of equations show that the solution to the system of equations 8x − 5y = 11 and 7x − 8y = 6 is the same as the solution to the given system of equations show that the solution to the system of equations 15x + 13y = 17 and 7x − 8y = 6 is the same as the solution to the given system of equations show that the solution to the system of equations −13x + 15y = 17 and 7x − 8y = 6 is the same as the solution to the given system of equations

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Mathematics, 14.07.2019 22:30, cman8228

(05.02) a system of equations is shown below: 5x + 2y = 3 (equation 1) 2x − 3y = 1 (equation 2) a student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. if equation 2 is multiplied by 1, which of the following steps should the student use for the proof? (4 points) select one: a. show that the solution to the system of equations 7x − y = 4 and 2x − 3y = 1 is the same as the solution to the given system of equations b. show that the solution to the system of equations 2x + 5y = 3 and 3x − 2y = 1 is the same as the solution to the given system of equations c. show that the solution to the system of equations 9x + 4y = 5 and 7x − y = 4 is the same as the solution to the given system of equations d. show that the solution to the system of equations −4x + 9y = 5 and 2x − 3y = 1 is the same as the solution to the given system of equations

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Mathematics, 23.10.2019 20:00, salvadorperez26

Find the solutions of the congruence 12x2 + 25x ≡ 10 (mod 11). [hint: show the congruence is equivalence to the congruence 12x2 + 25x + 12 ≡ 0 (mod 11). factor the left-hand side of the congruence; show that a solution of the quadratic congruence is a solution of one of two different linear congruences.]

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