Authors: Prashanth R. Rao
Collatz conjecture states that starting with any positive integer n, we divide it by 2 if it is even or multiply it by 3 and add 1 if it is odd and repeat this algorithm on the answer always using the same odd or even rule, we will ultimately end up with an answer of 1. Here we prove this conjecture for a special integer which is the product of any prime number “p” greater than three with another positive odd integer “x” that has been derived by using the Fermat’s little theorem and is therefore unique for each prime. Thus we prove Collatz’s conjecture for a small fraction of positive integers “px” which would be expected to roughly represent the same proportion of integers as prime numbers.
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[v1] 2014-12-30 14:23:47
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