Question

Solve the following systems of congruences.

x ≡ 2 mod 3

x ≡ 3 mod 4

Answer #1

Solve the system of congruences:
x = 1 (mod 3)
x = 2 (mod 4)
x = 2 (mod 5)

Solve the system of congruences
3x+4= 2 (mod 7)
x-13= 24 (mod 29)

solve the system of the congruences using Chinese Remainder.
x≡2 (mod 11)
x≡8 (mod 13)
x≡5 (mod 16)

solve the following set of simultaneous congruence x=1
mod (2) x= 2 mod(3) x =3:mod (5) x= 4 mod (11)

Using Chinese Remainder Theorem solve for X:
x = 2 (mod 3)
x = 4 (mod 5)
x = 5 (mod 8)
I have the answer the professor gave me, but I can`t understand
what`s going on. So if you could please go over the answer and
explain, it would help a lot.
x = 2 (mod 3)
x = 3a + 2
3a + 2 = 4 (mod 5)
(2) 3a = 2 (2) (mod 5) -----> why number...

(a) Solve
x ≡ 11 (mod 12), x ≡ 4 (mod 5), x ≡ 0 (mod 7)
(b) Find all the solutions of the following system:
x ≡ 5 (mod 6), x ≡ 4 (mod 11), x ≡ 3 (mod 17).

Find all solutions to the following sets of simultaneous
congruences
(a) x ≡ 10 mod 27 and x ≡ 172 mod 243
(b) x ≡ 10 mod 27 and x ≡ 172 mod 243 and x ≡ 163 mod 225
(c) x ≡ 10 mod 27 and x ≡ 172 mod 243 and x ≡ 162 mod 225

Solve the linear congruence
x = 2 mod (7)
x = 1 mod (3)

Solve each of the following congruences or explain why it is not
solvable:
(i) x2 + 5x + 7 ≡ 0(mod 41).
(ii) x2 ≡ 11(mod 125)

Solve (a) x^3=7 (mod 16), (b) x^3=12 (mod 27).

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 30 minutes ago

asked 36 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago