Question

Find all solutions in positive integers of the Diophantine
equation x^{2} + 3y^{2} = z^{2}

Answer #1

Use the Euclidean algorithm to find all integer solutions to the
following diophantine equation:
2x + 6y - 9z = 13
Find all positive integer solutions to the following diophantine
equation:
2x + 6y + 5z = 24

In this problem, consider the Diophantine equation: 703 = 30x +
11y.
(a) Describe ALL integer solutions.
(b) Describe ALL positive integer solutions i.e. x, y integers
with x > 0 and y > 0 making the equation true.

1a) Find all the integer solutions of each of the following
linear Diophantine equations:
(i) 2x + y = 2,
(ii) 3x - 4y = 0,
and
(iii) 15x + 18 y =17.
1b) Find all solutions in positive integers of each of the
following linear Diophantine equations:
(i) 2x + y = 2,
(ii) 3x - 4y = 0,
and
(iii) 7x + 15 y = 51.

Find all solutions to the equation cos ?z2 + 1? = i.

Find equations of the following.
x2 − 3y2 + z2 + yz =
52, (7, 2, −5)
(a) the tangent plane
(b) parametric equations of the normal line to the given surface at
the specified point. (Enter your answer as a comma-separated list
of equations. Let x, y, and z be in
terms of t.)

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)

Prove that there are no solutions in positive integers to the
equation x3 + y3 = 100

Find all positive integers x and y that satisfy x2 -
y2= 2018? Are there any positive integers x and y such
that x3 − y3 = 2018? Explain.

For each of the following linear Diophantine equations either
find all solutions or show that there are 97x+98y=1000

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 8 minutes ago

asked 12 minutes ago

asked 15 minutes ago

asked 18 minutes ago

asked 18 minutes ago

asked 36 minutes ago

asked 41 minutes ago

asked 43 minutes ago

asked 47 minutes ago

asked 53 minutes ago

asked 53 minutes ago