Question

Find the first two positive solutions to the system of 3 congruence equations x ≡ 3 (mod 9) x ≡ 9 (mod 12) x ≡ 7 (mod 22) (notice how the m1, m2, m3 are not co-prime!)

Answer #1

1. (i) find all solutions for the following congruence 370x ≡ 80
(mod 200)
(ii) find the first two positive solutions to the system of 3
congruence equations
x ≡ 3 (mod 9) x ≡ 9 (mod 12) x ≡ 7 (mod 22)
(notice how the m1, m2, m3 are not co-prime!)

Find all solutions to each congruence.
(a) 2x − 3 ≡ 2 (mod 7)
(b) 3x + 4 ≡ 1 (mod 5)
(c) 3x ≡ 6 (mod 9)
(d) 14x ≡ 11 (mod 15)

For each part, find all possible solutions to the given
equations (if any exist).
i ) x = 7 mod 9, x =3 mod 4
ii) 3x^2 +1 = 0 mod 10
iii) 3x+7 = 9 mod 10

Find all solutions to the polynomial congruence x^3 + x ≡ 50
(100).

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...

Solve the system of equations. Find all solutions. 5x + 7y = 31
x 2 + y 2 = 13

Solve 2sin(x)=3−4cos(x) for the first 2 positive solutions.

q.1.(a)
The following system of linear equations has an infinite number
of solutions
x+y−25 z=3
x−5 y+165 z=0
4 x−14 y+465 z=3
Solve the system and find the solution in the form
x(vector)=ta(vector)+b(vector)→, where t is a free
parameter.
When you write your solution below, however, only write the part
a(vector=⎡⎣⎢ax ay az⎤⎦⎥ as a unit column vector with the
first coordinate positive. Write the results accurate to
the 3rd decimal place.
ax =
ay =
az =

(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 the smallest positive integer x such that: x mod 2=1 x mod
3=2 and x mod 5=3
What is the next integer with this property?

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