Use the given formula to prove

Reference no: EM131350745

Use the formula for r₂(n) to prove the following:

(a) If n = p, where p is a prime of the form 4k + 1, then r₂(n) = 8. This implies that n can be written in a unique way as n = n₁² + n₂², except for the signs and reordering of n₁ and n₂.

(b) If n = q^a, where q is prime of the form 4k + 3 and a is a positive integer, then r₂(n) > 0 if and only if a is even.

(c) In general, n can be represented as the sum of two squares if and only if all the primes of the form 4k + 3 that arise in the prime decomposition of n occur with even exponents.

Reference no: EM131350745

Questions Cloud

The productivity analysis of handloom industry : how can we do the productivity analysis of handloom industry

How does sound play a role in movie back to the future : How does sound play a role in the movie Back To The Future? Editing of sound, music, sound effects, etc

Consider a capital budgeting problem with six project : Consider a capital budgeting problem with six project represented by binary (0 or 1) variables X1, X2, X3, X4, X5, X6.

Compare the originality of files in usb drive by calculating : To collect the evidence (data acquisition) from a USB drive which has been deleted by actor in order to remove all evidences against a crime they committed using Prodiscover tool.To compare the originality of the contents of files in storage device..

Use the given formula to prove : Use the formula for r2(n) to prove the given:- If n = p, where p is a prime of the form 4k + 1, then r2(n) = 8. This implies that n can be written in a unique way as n = n12 + n22, except for the signs and reordering of n1 and n2.

Determining the international management : Discuss the appropriateness of using the same leadership style across all EU countries. Include in your discussion the research results for different views given in your textbook.

What is the mass flow rate under these conditions : What is the minimum stagnation temperature required to avoid air condensation in the working section (the condensation temperature under these conditions is about 70°K)?

The market price of security-constant dividend in perpetuity : The market price of a security is $62. Its expected rate of return is 11%. The risk-free rate is 6%, and the market risk premium is 7%. What will the market price of the security be if its beta doubles (and all other variables remain unchanged)? Assu..

Internal auditor and the independent auditor : Compare and contrast the roles of the internal auditor and the independent auditor. What would you include in you report for internal auditing, if you are the CFO of your hospital?

User Account

All Pages