How to Prove The Collatz Conjecture [Paperback]

Danny Fleming (Author)

Book Description

Publication Date: March 17, 2005

The first proof of the Collatz Conjecture.

Editorial Reviews

About the Author

I have a Bachelor of Science in Mathematics and a Classical Studies Minor I received from Califorina State University in 1996.

Excerpt. © Reprinted by permission. All rights reserved.

... First, any even number will continue decreasing until it reaches 1 or an odd number. Once we reach this odd number x, we will have an even number after the 3x+1 rule is applied. Here is why: We know 3 is always odd by definition. And x is always odd because the 3x+1 rule is always used if x is odd. For the 3x part of 3x+1, we have an odd number (3) times another odd number (x). We know from Book IX Proposition 29 of Euclid's Elements that an odd number times another odd number is always odd. Examples, using 3 and any other positive odd integer for 3x+1 are: 3x3=9, 3x9=27, 3x81=243, 3x5=15, 3x19=57, etc. As expected, 9, 27, 243, 15, 57 are all odd ... Adding 1 to this proven odd 3x will always be an even number because any odd number plus 1 is even ... .

Product Details

• Paperback: 149 pages
• Publisher: Lulu.com (March 17, 2005)
• Language: English
• ISBN-10: 141160427X
• ISBN-13: 978-1411604278
• Product Dimensions: 9 x 6 x 0.4 inches
• Shipping Weight: 8 ounces (View shipping rates and policies)
• Amazon Best Sellers Rank: #3,628,526 in Books (See Top 100 in Books)

More About the Author

Danny Karl Fleming was born on May 25, 1948 in Long Beach, California. He received a Bachelor of Science in Mathematics and a Classical Studies Minor
from California State University, Long Beach in 1996. He has been a successful tutor in mathematics online. He has devised a formula that finds
delays of the Collatz Conjecture. He is currently working on finding
large prime numbers. He is a good chess player and enjoys listening to classical music. Two books written by Danny Fleming are How to Prove The Collatz Conjecture and How to Prove The Goldbach Conjecture. Four
poems are by Danny Fleming--Kasparov's Doom, I Tell You Be A Clown, My Love,
and I Don't Remember. Kasparov's Doom is a limerick, I Don't Remember
has the Elizabethan sonnet rhyming pattern and I Tell You Be A Clown has
the Elizabethan sonnet rhyming and rhythmical pattern.