# Ramanujan's Proof of Bertrand's Postulate

@article{Meher2013RamanujansPO, title={Ramanujan's Proof of Bertrand's Postulate}, author={Jaban Meher and M. Ram Murty}, journal={The American Mathematical Monthly}, year={2013}, volume={120}, pages={650 - 653} }

Abstract We present Ramanujan's proof of Bertrand's postulate and in the process, eliminate his use of Stirling's formula. The revised proof is elegant and elementary so as to be accessible to a wider audience.

## 4 Citations

Bertrand's Postulate for Number Fields

- Mathematics
- 2015

Consider an algebraic number field, $K$, and its ring of integers, $\mathcal{O}_K$. There exists a smallest $B_K>1$ such that for any $x>1$ we can find a prime ideal, $\mathfrak{p}$, in…

On Deciding Linear Arithmetic Constraints Over p-adic Integers for All Primes

- Mathematics, Computer ScienceMFCS
- 2021

A coNEXP upper bound for both problems, together with a matching lower bound for existential Buchi arithmetic are obtained from analysing properties of a certain class of p-automata, finite-state automata whose languages encode sets of tuples of natural numbers.

The Full Automorphism Groups, Determining Sets and Resolving Sets of Coprime Graphs

- MathematicsGraphs Comb.
- 2019

This paper first determines the full automorphism group of the coprime graph, and then finds the regularities for a set becoming a determining set or a resolving set in a coprimes graph.

Decomposing Permutation Automata

- Computer Science, MathematicsCONCUR
- 2021

An NP algorithm is provided to decide whether a permutation DFA is composite, and it is shown that, for commutative permutation DFAs, restricting the number of factors makes the decision computationally harder, and yields a problem with tight bounds: it is NP-complete.

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This content downloaded from 61.95.189.187 on Wed, 7 Aug 2013 12:45:04 PM All use subject to JSTOR Terms and Conditions

- This content downloaded from 61.95.189.187 on Wed, 7 Aug 2013 12:45:04 PM All use subject to JSTOR Terms and Conditions