Question

solve the system of the congruences using Chinese Remainder.

x≡2 (mod 11)

x≡8 (mod 13)

x≡5 (mod 16)

Answer #1

here we want to find an x such that it satusfy all congruences givens.since modulis 11,13,16 are relatively prime in pairs we can apply chinese remainder theorem.

Ans) x=1685+2288k where k is an integer.

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

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

(20 pts) Use construction approach in the proof of the Chinese
Remainder Theorem to solve system of congruences ? ≡ 2 (mod 3) and
? ≡ 1 (mod 4) and ? ≡ 3 (mod 5).

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...

Solve the following systems of congruences.
x ≡ 2 mod 3
x ≡ 3 mod 4

(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).

Question 1
Consider the system of congruences x ≡ 19 (mod 23),
x ≡ 8 (mod 29). The smallest positive solution to this
system is......
Question 2
Out of 8 consonants and 5 vowels, the number of words of 2
consonants and 2 vowels can be formed is .......
Question 3
In a group of 7 men and 8 women, a committee with 5 people is to
be selected. The number of ways to form this committee so that at...

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

***PLEASE SHOW ALL WORK AND COMMANDS FOR HOW TO DO IN
SAGE APPLICATION***
Use the construction in the proof of the Chinese remainder
theorem to find all solutions to the system of congruences
x ≡ 1 (mod 2)
x ≡ 2 (mod 3)
x ≡ 3 (mod 5)
x ≡ 4 (mod 11).

Find all, if any, solutions to the system:
x ≡ 5 (mod 5)
x ≡ 3 (mod 7)
x ≡ 8 (mod 11)
x ≡ 2 (mod 17)
need help with discrete math HW, please write solutions clearly,
and please don't just answer wrong solution, cus then i will need
to post the same question twice. i appreciate every help i can get
but please let someone else help me solve the question if you're
not sure about any part...

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