Number Theory


Another Proof for Catalan's Conjecture

Authors: Julian Beauchamp

In 2002 Preda Mihailescu used the theory of cyclotomic fields and Galois modules to prove Catalan's Conjecture. In this short paper, we give a very simple proof. We first prove that no solutions exist for a^x-b^y=1 for a,b>0 and x,y>2. Then we prove that when x=2 the only solution for a is a=3 and the only solution for y is y=3.

Comments: 3 Pages.

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Submission history

[v1] 2018-12-19 05:32:58
[v2] 2018-12-19 06:26:14

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