Do odd perfect numbers exist?
These sources were particularly helpful:
Perfect numbers via MacTutor -
Cai, T. (2022). Perfect numbers and fibonacci sequences. World Scientific. -
Dunham, W. (2022). Euler: The master of us all (Vol. 22). American Mathematical Society. -
▀▀▀
References:
Dickson, L. E. (1919). History of the Theory of Numbers.. (Vol. 1). Carnegie Institution of Washington.
Knill, O. (2007). The oldest open problem in mathematics. NEU Math Circle, December2. -
Perfect number via Wikipedia -
Introduction to Arithmetic via HalthiTrust -
Nicomachus of Gerasa via MacTutor -
Sonja, B. (1988). The First Perfect Numbers and Three Types of Amicable Numbers in a Manuscript on Elementary Number Theory by Ibn Fellûs. Erdem, c. IV, 11. -
Ibn Fallus via Wikipedia -
Mersenne prime via Wikipedia -
List of Known Mersenne Prime Numbers -
Marin Mersenne via MacTutor -
Leonhard Euler via Wikipedia -
Frank Nelson Cole via Wikipedia -
GIMPS History via -
EFF Cooperative Computing Awards via EFF -
Jonathan Pace via Primewiki -
Book with just one number sells out in Japan via BastillePost -
Predicted distribution of Mersenne primes via John D. Cook -
Euler’s Odd Perfect Numbers Theorem via Cantor’s Paradise -
A Perfect (Math) Mystery via Medium -
Brent, R. P., Cohen, G. L., & te Riele, H. J. (1991). Improved techniques for lower bounds for odd perfect numbers. Mathematics of Computation, 57(196), 857-868. -
Ochem, P., & Rao, M. (2012). Odd perfect numbers are greater than 10¹⁵⁰⁰. Mathematics of Computation, 81(279), 1869-1877. -
Mathematicians Open a New Front on an Ancient Number Problem via Quantamagazine -
Descartes number via Wikipedia -
Andersen, N., Durham, S., Griffin, M. J., Hales, J., Jenkins, P., Keck, R., ... & Wu, D. (2022). Odd, spoof perfect factorizations. Journal of Number Theory, 234, 31-47. -
Pomerance’s Heuristic that Odd Perfect Numbers are Unlikely via -
165 views
20
6
5 months ago 00:05:20 1
Shugyo: Naginata in New York
5 months ago 00:00:12 2
oldest trick in the book 🤠
5 months ago 01:14:44 1
Didgeridoo Dreamtime ( Psydub,Tribal,Chill Out | 2024 )
5 months ago 00:02:30 1
Where You’re Meant To Be (Official Trailer)
5 months ago 00:45:07 1
Clown Dimitri - “Le Porteur“ (“The Porter“, 1988)
5 months ago 00:02:44 1
The Sound the Tocharian language (Numbers, Greetings, Phrases & An Excerpt)