International Journal of Mathematics Trends and Technology
Volume 67 | Issue 7 | Year 2021 | Article Id. IJMTT-V67I7P521 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I7P521
Lothar Collatz introduced Collatz Conjecture in 1937. No one succeeded in proving this conjecture. In this article a convincing mathematical proof is introduced. Initially it is proved that for every natural number n in N={1,2,3,..}, the set An exists where An ={x/x is a term in Hailstone sequence starting with n}. Later it is proved thatthe intersections of An and Am is not empty foreverynatural number nā m, m,n >1. Then it is observed that the countable intersection of all An contains A0= {1}.This observation brings the conclusion that for all Hailstone sequences starting with any positive integer n ,there exists a a term 1 in the Hailstone sequence.This conclusion implies that for any positive integerš, the Hailstone sequence starting with n eventually ends in 1.
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Nishad T M, "Mathematical Proof of Collatz Conjecture," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 7, pp. 178-182, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I7P521
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