Please see the attached file.
Show that if p is prime an x^2+5y^2=p, then (p/5)=1 where (p/5) denotes the Legendre symbol.
Show that if p is prime an x^2+5y^2=p, then (p/5)=1 where (p/5) denotes the legendre symbol.
Binomial Expansiosna nd Estimating Cube Roots
Write out the first five terms in the binomial expansion of (1+x)^(1/3) Use it to get an estimate of (70)^(1/3) .
Please see the attached Microsoft Word document. Thanks for your expertise.
Find all integers n such that φ(n) = 37.
Number Theory : Quadratic Residues
Please provide a detailed solution to the attached problem. Please do not give a trivial answer. I think the questions asks us to determine the what form p is of (for example, p is a prime of the form 3n+1 (this was an example randomly chosen). I am trying to solve this problem myself (using that x^2-6 = 0 (mod p) => 6 is a quad ...continues
Fermat's Little Theorem and Binomial Theorem
Show that every odd prime except 5 divides some number of the form 111...11 (k digits long, all ones).
Explain the Law of Large Numbers
A. Define the Law of Large Numbers. B. Explain the Law of Large Numbers in your own words using a coin toss as an example. C. Apply the Law of Large Numbers 1. Explain how the following scenario is possible, using a coin toss and fictitious data: As the number of trials increases, the differences between the number ...continues
I need help with this problem. It has two parts a) and b). (a) Show that if m is a number having primitive roots, then the product of the positive integers less than or equal to m and relatively prime to is congruent to -1(mod m). (b) Show that the result in (a) is not always true if m does not have primitive roots. ...continues
Please see the attached problem. Thanks in advance for your help. 1. Show that if m and n have a common factor greater than 1. Please show all work, provide as much information as possible. I am studying for an exam, so I really need to understand how to work this problem.
