Purchase Solution

Theory of numbers

Not what you're looking for?

Ask Custom Question

Use Quadratic Congruences to evaluate the following fractions. See attached file for full problem description.

Attachments
Purchase this Solution

Solution Summary

The solution involves the result concerning quadratic congruences.

Solution Preview

Please see the attached file.

Euler's Criterion
Let p be an odd prime and let a be an integer not divisible by p. If a is a square modulo p, then . If a is not a square modulo p, then

Quadratic Residues:
Let p be a prime, and let a be an integer not divisible by p. If a is a square modulo p, then a is said to be a quadratic residue modulo p. Otherwise, we say that a is a quadratic nonresidue modulo p.

Legendre symbol:
Let p be a prime, and let a be an integer. The Legendre symbol is defined by

Theorem ...

Purchase this Solution


Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.