Ramanujan: congruences for the partition function

What changed

Proved the modulo 5 and modulo 7 partition congruences and stated a wider family of congruence phenomena for the partition function.

Scientific scope

The record is the exact 1919 Cambridge Philosophical Society paper. The Hardy–Ramanujan asymptotic formula, Ramanujan’s later partition memoir and posthumous congruence paper remain separate.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is the exact 1919 Cambridge Philosophical Society paper. The Hardy–Ramanujan asymptotic formula, Ramanujan’s later partition memoir and posthumous congruence paper remain separate.

Contributors

• Srinivasa Ramanujan · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• Ramanujan paper 25: Some properties of p(n)
• Ramanujan, Some properties of p(n), PDF

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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