Mordell Equations
Not what you're looking for?
Exercise 5. The aim of this exercise is to prove that the Mordell equation y^2 = x^3 - 5 has no solutions. We proceed by contradiction and assume that (x, y) is an integral solution.
1. By reducing Mordell equation mod 4, show that y is even and x = 1 mod 4.
2. Show that y^2 + 4 = (x-1)(x^2 + x +1)
3. Show that x^2 + x + 1 is congruent to 3 mod 4 and that x^2 + x + 1 greater than 3
4. Prove that x^2 + x + 1 has a prime factor p congruent to 3 mod 4
See attachment for remainder of problem set.
Purchase this Solution
Solution Summary
In this solution, a particular situation of Mordell equation is discussed with steps given to solve the problem set.
Solution Preview
1. Assuming there is a solution, we reduce the equation to modulo 4.
We tabulate the values of x and y as ...
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Probability Quiz
Some questions on probability
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.