Question

500X+423Y=1 Diophantine equation

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

Find all solutions in positive integers of the Diophantine
equation x2 + 3y2 = z2

NUMBER THEORY
1. Solve the following diophantine equation 18x-14y=8
for a general solution.
2. Solve the following congruence x+12≡ 5(mod 8) for a
general solution.

Find a solution to the Diophantine equation or explain why no
solution exists.
105X+91Y=7

how
would you solve the below diophantine equation using thw method of
congruence. - number theory
Show that the equation 11x^2 + 10x - y^2 + 2 = 0 has no
solutions.

Find the general solution for the diophantine equation (do not
use trial and error) 1.44x+2.49y=552.75 see question below
The Student’s Union at the Pythagorean School wants to buy as
many pens and notebooks as are available at the agora. Homer, the
Education Officer, finds that the price of a pen is €1.44 while the
price of a notebook is €2.49. He buys all the available pens and
notebooks and on his return to the school discovers that in total
he...

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

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.

Which of the following Diophantine equations cannot be solved?
(Show all work.)
6 x + 51 y = 22
33 x + 14 y = 115
14 x + 35 y = 93

State whether each of the following is true or false:
a) Today we know that the Fermat number 225 + 1 is prime.
b) The Fermat Primes are important in geometry.
c) Fermat’s Last Theorem states that the nonlinear Diophantine
equation xn + yn = zn has no nonzero integral solutions for n >
2.
d) The nonlinear Diophantine equation x2+y2 = z2 has no integral
solutions.
e) As of 2010, a total of 243 Fermat Numbers are known to...

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