Lagrange's theorem
Not what you're looking for?
Suppose that...
Use Lagrange's Theorem
Suppose that a N and
a z (mod pq) where p q 3(mod 4 ) are primes.
Prove that there are only four possible square roots of a modulo pq, and they are given as follows. For x,y Z given by the extended Euclidean Algorithm, such that xp +yq =1
We have
Z= (xpa + yqa ), and Z= (xpa - yqa )
Use Lagrange's Theorem
Purchase this Solution
Solution Summary
This is a proof involving Lagrange's theorem.
Solution Preview
Please see the attachment.
Proof:
The equation (mod ) is equivalent to the system of equations
(mod ) and (mod )
Now let's consider the equation (mod ). It has two solutions if is a quadratic residue module . Since ...
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
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.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Probability Quiz
Some questions on probability
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts