Explanation for the Number Cycle that was Introduced by Mohammadreza Barghi
Abstract: Previously I introduced a number cycle that takes two consecutive integers and a third integer that after a cycle of some operations including adding and dividing, returns one of the two consecutive integers. Here I am explaining how it works. If you add integer "a" to integer "b" and then divide it by two, the result could be written as follows i.e.: (b + a) / 2 = ( b + a) /2 +( - a + a) = (b/2 + a/2 - a) + a = ( (b-a)/2 + a. In the next operations, this result substitutes "b", and if you add this new "b" to "a" and divide it by 2, it will be: (((b - a)/2 + a) + a)/2⤏((b -a)/2 + a + a)/2⤏(b - a)/4 + ( a + a)/2⤏(b - a) / 4 + a. Repeating this cycle causes that (b - a)/2^n (n is the number of repeating of (b -a)/2) ends to 1 or -1 depending if b>a or b
Keywords: number theory, integer, numerical, collatz
How to Cite?: Mohammadreza Barghi, "Explanation for the Number Cycle that was Introduced by Mohammadreza Barghi", Volume 12 Issue 1, January 2023, International Journal of Science and Research (IJSR), Pages: 1032-1033, https://www.ijsr.net/getabstract.php?paperid=SR23125040154, DOI: https://dx.doi.org/10.21275/SR23125040154