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Journal of Pure and Applied Mathematics

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A proof of Collatz’s Conjecture

Author(s): Ramaswamy Krishnan

The proof of Collatz Conjecture is divided in to three parts. In the First part it is proved for the set of numbers {1, 5, 21, 85}. In the second part, using the above it is proved for odd numbers of the form (4k+1). In the third part it is shown how numbers of the form (4k+3) iterates in to numbers of the form (4k+1). Thus the Conjecture is proved for all odd ‘n’. As even numbers iterate into Odd numbers, the Conjecture is proved for all positive integers.


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