Question

Does the equation x^{2} + 5x≡ 13 (mod 34) have
solutions? Can you ﬁnd the solution?

Answer #1

Which of the following congruences have solutions?
a) x2 Congruent 7(mod 53)
b) x2 Congruent 14(mod 31)
c) x2 Congruent 53(mod 7)
d) x2 Congruent 25(mod 997)
All of them please!!

Show that the equation x2+y2+z2
= 7 has no integer solutions.
(Using mod)

Show that the equation x2+y2+z2
= 7 has no integer solutions.
(Without mod)

Find all solutions to the system:
2x ≡ 4 (mod 5)
3x ≡ 5 (mod 7)
7x ≡ 2 (mod 13)
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 to avoid reposting. thanks, will rate best...

For each of the following congruences if there is a solution,
express the solution in the form x
≡ some_number (mod
some_modulus), e.g. x ≡ 6 (mod 9). To standardize
answers, some_number should always be a value
in the range {0, 1, 2, ..., some_modulus -1}. For example
x ≡ 5 (mod 8) is OK but x ≡ 13 (mod 8) is not.
If there is no solution say "No solution". You don't have to
show work for any of the problems. Type...

1. If x1(t) and x2(t) are solutions to the differential
equation
x" + bx' + cx = 0
is x = x1 + x2 + c for a constant c always a solution? Is the
function y= t(x1) a solution?
Show the works
2. Write sown a homogeneous second-order linear differential
equation where the system displays a decaying oscillation.

If x1(t) and x2(t) are solutions to the differential
equation
x"+bx'+cx = 0
1. Is x= x1+x2+c for a constant c always a solution?
(I think No, except for the case of c=0)
2. Is tx1 a solution? (t is a constant)
I have to show all works of the whole process, please
help me!

For which integers c, 0 ≤ c < 30, does the congruence 12x ≡ c
(mod 30) have at least one solution? Give the solutions for each
such c.

How many different integer solutions are there to the equation
x1 + x2 + x3 + x4 + x5 + x6 + x7 = 23, 0 ≤ xi ≤ 9 ?
(a) (2 points) Solve the problem by using Inclusion-Exclusion
Formula. (b) (2 points) Check whether your solution obtained from
part
(a) is right by using the generating function method.

for 7-9 you will solve the following system of equation :
2x+3u+z=17 x-3y+2z=-8 5x-2y+3z=5 7) what is the solution for x? a)2
b)1 c)infinitely many solution d)no solution 8)what is the solution
for y? a)4 b)2 c)inifinitely many solutions d)no solution 9) what
is the solution for z? a)9 b)1 c)inifinitely many solutions d)no
solution

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