# Proof of a conjecture of Ramanujan

```@article{Atkin1967ProofOA,
title={Proof of a conjecture of Ramanujan},
author={A. O. L. Atkin},
journal={Glasgow Mathematical Journal},
year={1967},
volume={8},
pages={14 - 32}
}```
• A. Atkin
• Published 1 January 1967
• Mathematics
• Glasgow Mathematical Journal
We write and so that p(n) is the number of unrestricted partitions of n. Ramanujan  conjectured in 1919 that if q = 5, 7, or 11, and 24m ≡ 1 (mod qn), then p(m) ≡ 0 (mod qn). He proved his conecture for n = 1 and 2†, but it was not until 1938 that Watson  proved the conjecture for q = 5 and all n, and a suitably modified form for q = 7 and all n. (Chowla  had previously observed that the conjecture failed for q = 7 and n = 3.) Watson's method of modular equations, while theoretically…
123 Citations
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