This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An...This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.展开更多
The 3x + 1 problem, is a math problem that has baffled mathematicians for over 50 years. It’s easy to explain: take any positive number, if it’s even, divide it by 2;if it’s odd, multiply it by 3 and add 1. Repeat ...The 3x + 1 problem, is a math problem that has baffled mathematicians for over 50 years. It’s easy to explain: take any positive number, if it’s even, divide it by 2;if it’s odd, multiply it by 3 and add 1. Repeat this process with the resulting number, and the conjecture says that you will eventually reach 1. Despite testing all starting values up to an enormous number, no one has proved the conjecture is true for all possible starting values. The problem’s importance lies in its simplicity and difficulty, inspiring new ideas in mathematics and advancing fields like number theory, dynamical systems, and computer science. Proving or disproving the conjecture would revolutionize our understanding of math. The presence of infinite sequences is a matter of question. To investigate and solve this conjecture, we are utilizing a novel approach involving the fields of number theory and computer science.展开更多
文摘This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.
文摘The 3x + 1 problem, is a math problem that has baffled mathematicians for over 50 years. It’s easy to explain: take any positive number, if it’s even, divide it by 2;if it’s odd, multiply it by 3 and add 1. Repeat this process with the resulting number, and the conjecture says that you will eventually reach 1. Despite testing all starting values up to an enormous number, no one has proved the conjecture is true for all possible starting values. The problem’s importance lies in its simplicity and difficulty, inspiring new ideas in mathematics and advancing fields like number theory, dynamical systems, and computer science. Proving or disproving the conjecture would revolutionize our understanding of math. The presence of infinite sequences is a matter of question. To investigate and solve this conjecture, we are utilizing a novel approach involving the fields of number theory and computer science.
