Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. let us divide the odd positive integers into two a

Let us divide the odd positive integers into two arithmetic progressions; the red numbers are 1,...

50.1K

Verified Solution

Question

Advance Math

Let us divide the odd positive integers into two arithmeticprogressions; the red numbers are 1, 5, 9, 13, 17, 21, ... The bluenumbers are 3, 7, 11, 15, 19, 23,....

(a) Prove that the product of two red numbers is red, and thatthe product of two blue numbers is red.

(b) Prove that every blue number has a blue prime factor.

(c) Prove that there are infinitely many blue prime numbers.Hint: Follow Euclid’s proof, but multiply a list together, multiplythe result by four, then subtract one.

Answer & Explanation Solved by verified expert
3.8 Ratings (391 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

Statement of Cash Flows—Indirect MethodThe comparative balance sheet of Merrick Equipment Co. forDecember 31,...Statement...

Accounting
Q

What is the molarity of a sodium hydroxide solution if 25.0 ml of this solution reacts...

Chemistry
Q

Explain why negative or harmful mutations have no role in the evolution of a population. How do...

Biology
Q

How does a file drawer analysis (see book for description of “file drawer”) make the findings...

Basic Math
Q

Which of the following is translated in the cytoplasm and then imported into an organelle...

Biology
Q

18 Four holes of radius R are cut from a thin square plate of side...

Physics
Q

10 A car depreciates in value according to the model V 25000 0 85 where...

Basic Math
Q

What are the solutions to the equation 2 0 25x 4x 0 75 Round to...

Algebra
Q

Sales Mix and Break-Even Analysis Heyden Company has fixed costs of $849,300. The unit selling...

Accounting
Q

Question 23 hole pro oprietor runs 1 points SAVE DON.BA a. are ar o and...

Accounting
Q

Smith Company exchanges assets to acquire a building. The market price of the Smith stock...

Accounting
Q

Which convention is used for the year of disposition for a warehouse? A. Mid-quarter b....

Accounting