Mathematical Proof of Collatz Conjecture International Journal of Mathematics Trends and Technology (IJMTT) © 2021 by IJMTT Journal Volume-67 Issue-7 Year of Publication : 2021 Authors : Nishad T M 10.14445/22315373/IJMTT-V67I7P521 MLA Style: Nishad T M"Mathematical Proof of Collatz Conjecture" International Journal of Mathematics Trends and Technology 67.7 (2021):178-182.

APA Style: Nishad T M(2021). Mathematical Proof of Collatz Conjecture International Journal of Mathematics Trends and Technology, 178-182.

Abstract
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 n≠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 integer n, the Hailstone sequence starting with n eventually ends in 1.

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Keywords : Collatz conjecture, Lothar Collatz, Hailstone sequence, 3n+1, n/2 function,Proof of Collatz Conjecture