The Ramanujan-Nagell equation asks for integer solutions of 2 to the n minus 7 equals x squared, and it has exactly five solutions, at n equal to 3, 4, 5, 7 and 15, corresponding to x equal to 1, 3, 5, 11 and 181. Srinivasa Ramanujan first conjectured in 1913 that these were the only solutions, Wilhelm Ljunggren proposed the same claim independently in 1943, and Trygve Nagell proved it in 1948. As an exponential diophantine equation with only finitely many solutions, it has influenced the study of related equation families, and it also implies the non-existence of perfect binary codes with minimum Hamming distance 5 or 6. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementThe equation 2^n - 7 = x^2 has solutions in natural numbers n and x only for n = 3, 4, 5, 7 and 15. 1 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
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Source Ramanujan-Nagell equation (Wikipedia)
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1. Ramanujan-Nagell equation (Wikipedia)
Equation and solution, first paragraph
solutions in natural numbers n and x exist just when n = 3, 4, 5, 7 and 15
Equation and solution, second paragraph
proved in 1948 by the Norwegian mathematician Trygve Nagell
- In Branch: Number Theory, Lead sentence
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