Question: (b) Prove that if there exist positive integers m, n satisfying the equation 3m = n2 - 40, then m must be even. Hence find

(b) Prove that if there exist positive integers m, n satisfying the equation 3m = n2 - 40, then m must be even. Hence find all positive integral solutions of the equation 3m = n2 - 40

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Answer 6.1, 6.3, 6.4, 6.6, 6.9, 6.14, 6.15, 8.1, 8.5, 8.8, 8.13, and 8.19 Problem 6.1 Show that there exist integers m and n such that 3m + 4n = 25. Problem 6.2 Show that there is a positive integer...

HW 12, MAT 312/AMS 351: SPRING 2017 Problem 1. (1) Set H = {4a + 6b | a, b Z} Z. Show that H is a subgroup of Z. (2) Is H cyclic? Problem 2. Write down all the cyclic subgroups of the following...

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

\fsh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Math 280 Strategies of Proof Fall 2007 Class Notes 3.6 Proving Conditional Statements II: Indirect Proofs In Section 3.4, we studied...

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

9/14/10 12:27 PM Page 321 Chapter dug84356_ch05a.qxd 5 Factoring The sport of skydiving was born in the 1930s soon after the military began using parachutes as a means of deploying troops. Today,...

1) Find all real solutions of: 4 2 2 x + x =3 2 x 4 + x23=0 4 2 2 2 x 2 x +3 x 3=0 x ( 21)=0 2 x 2 ( x 21)+ 3 ( 2 x2 +3 ) ( x 21 ) =0 ( 2 x2 +3 ) =0 2 2 x =3 3 x 2= 2 3 x= 2 3 x= i 2 2) Given the...

(a) The wavelength of light incident on a metal surface is reduced from 1 to, 2. (Both 1 and 2 are less than the threshold wavelength for the surface.) When the wavelength is reduced in this way,...

Suppose that Sanders Co., a U.S.-based MNC, is considering options to finance its U.S. operations with a one-year loan. Sanders bank offers a oneyear loan in U.S. dollars at an interest rate of...

A ( n ) ) is a firm that pools the money of investors to invest in real estate or make cor struction or mortgage loans. It is similar to a mutual fund. Dral extate syndicate n . at ecte hourtment...

Angel Suarez is meeting with team members to hear their ideas on improving company benefits. Angel wants to be sure her team knows that she hears what they're saying, especially when it comes to the...