| Title | Citation |
|---|---|
| Perfect Numbers and Perfect Polynomials | Abu-Arish, H. (2016). Perfect Numbers and Perfect
Polynomials: Motivating Concepts from Kindergarten to College. Ohio State University. Retrieved from https://etd.ohiolink.edu/!etd.send_file?accession =osu1461154144&disposition=inline |
| Table of Known Mersenne Primes | Caldwell, C.K. “The Table of Known Mersenne
Primes.” University of Tennessee at Martin. (26 December 2017). https://primes.utm.edu/mersenne/. |
| Perfect Number | The Editors of Encyclopaedia Britannica.
(2004). Perfect Number. Encyclopaedia Britannica. Retrieved from https://www.britannica.com/science/perfect-number |
| Perfect Numbers | French, D. (2010). Perfect Numbers. University of
Nebraska-Lincoln. Retrieved from http://digitalcommons .unl.edu/cgi/viewcontent.cgi?article=1012&context=math midexppap |
| Info on Perfect Numbers | Garcia, A. “On Perfect Numbers.” Department of Mathematics
and Computer Science. Saint Mary’s College of California, (17 May 2016). Retrieved from, http://math.stmarys-ca.edu/ wp-content/uploads/2017/07/Arturo-Garcia.pdf. |
| Odd Perfect Numbers | Heath-Brown, D.R. (1994). Odd Perfect Numbers.
Mathematical Proceedings of the Cambridge Philosophical Society, Volume 115 (Issue 2). Retrieved from https://www.cambridge.org/core /journals/mathematical-proceedings-of-the-cambridge -philosophical-society/article/odd-perfect-numbers/ 5FA21CDC2F3D0922D6A4589CC918E7DE |
| Archimedes Revenge | Hoffman, J. (1988). Archimedes Revenge: The Joys and
Perils of Mathematics. W.W. Norton & Co., Inc. New York. |
| Mersenne Prime | Hosch, W.L. (2009). Mersenne Prime.
Encyclopaedia Britannica. Retrieved from https://www.britannica.com/science/Mersenne-prime |
| Perfect Numbers | Knoderer, J. (N.d.). Perfect Numbers.
The Math Forum. Retrieved from http://mathforum.org/dr.math/faq/faq.perfect.html |
| Perfect Numbers | (N.d.) Perfect Numbers. The Creativity of Mathematics.
Retrieved from http://creativityofmathematics.weebly. com/perfect-numbers.html |
| Triangular Numbers | Moat, J. “Triangular Numbers in the Classroom.”
University of Cambridge, (June 2013). Retrieved from https://nrich.maths.org/10010 |
| An Upper Bound for Perfect Numbers | Nielson, P.P. (2003). An Upper Bound for Odd
Perfect Numbers. European Mathematical Information Service. Retrieved from http://emis.ams.org/journals/INTEGERS/papers/d14/d14.pdf |
| Number Theory and its History | Ore, O. (1998). Number Theory and its History.
New York: Dover Publications, Inc. Retrieved from https://books.google.com/books?hl=en&lr=&id=Sl_6BP p7S0AC&oi=fnd&pg=PR5&dq=history+of+perfect+numbers& ots=_YPhEc_tkG&sig=5H1IgGZu9IFU3KuG3jy0hJUwruQ#v=one page&q=history%20of%20perfect%20numbers&f=false |
| On Perfect and Near-Perfect Numbers | Pollack, P., Shevelev, V. (2012). On Perfect and
Near-Perfect Numbers. Journal of Number Theory, Elsevier. Retrieved from https://www.math.bgu.ac.il/~shevelev/PollakShevelev12.pdf |
| The Pantheon | Ranogajec, P.A. (N.d.) The Pantheon. Khan
Academy. Retrieved from https://www.khanacademy. org/humanities/ancient-art-civilizations/ roman/middle-empire/a/the-pantheon |
| Number Game | Schaaf, W. L. (1999). Number game.
Encyclopaedia Britannica. Retrieved from https://www.britannica.com/topic/number-game#ref396131 |
| Unitary Perfect Numbers | Subbarao, M.V., Warren, L.J. (1965).
Unitary Perfect Numbers. Retrieved from https://books.google.com/books?hl=en&lr=&id =wWIOYPbx6JoC&oi=fnd&pg=PA147&dq=perfect+numbers &ots=BmgGdmJ9XC&sig=ZhCdAkG_uuuaeVqNFNcSh1hE7BU# v=onepage&q=perfect%20numbers&f=false |
| Perfect Numbers: An Elementary Introduction | Voight, J. (N.d.). Perfect Numbers: An Elementary
Introduction. Department of Mathematics, University of California, Berkeley. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi= 10.1.1.71.5417&rep=rep1&type=pdf |
| Perfect Graph | Weisstein, E. W. (N.d.). Perfect Graph.
MathWorld--A Wolfram Web Resource. Retrieved from http://mathworld.wolfram.com/PerfectGraph.html |
| Perfect Number | Weisstein, E. W. (N.d.). Perfect Number.
MathWorld--A Wolfram Web Resource. Retrieved from http://mathworld.wolfram.com/PerfectNumber.html |
| List of Perfect Numbers | Wikipedia. “List of Perfect Number.” Wikipedia,
2018. Retrieved from https://en.wikipedia.org/ wiki/List_of_perfect_numbers. |
| Descartes Number | (2018, Aug. 14). Descartes Number. Maths
Ed. Retrieved from https://mathsedideas. blogspot.com/2018/08/on-descartes-numbers.html |
| Title | Citation |
|---|---|
| nth Prime | Booker, A. (N.d.). The Nth Prime Page. The Prime Pages. Retrieved from
https://primes.utm.edu/nthprime/ |
| Prime Numbers | Earl, R. (2015, Jan. 15). Prime Numbers. Retrieved from https://podcasts.ox.ac.uk/prime-numbers |
| Perfect Number | Fattah, M. (2016, Dec. 18). Perfect Number. Retrieved from
https://www.youtube.com/watch?v=0p1QsPRJcAU |
| 8128 and Perfect Numbers | Haran, B. [Numberphile]. (2011, Nov. 28). 8128 and Perfect Numbers ~ Numberphile.
Retrieved from https://www.youtube.com/watch?v=ZfKTD5lvToE |
| Perfect Numbers Proof | Haran, B. [Numberphile]. (2015, Jan. 6). Perfect Numbers Proof ~ Numberphile.
Retrieved from https://www.youtube.com/watch?v=q8n15q1v4Xo |
| Perfect Numbers and Mersenne Primes | Haran, B. [Numberphile]. (2015, Jan. 6). Perfect Numbers and Mersenne Primes ~ Numberphile.
Retrieved from https://www.youtube.com/watch?v=T0xKHwQH-4I&vl=en |
| Buisiness Insider Article | Kiersz, A. (2018). Google Hid Another Nerdy Math Joke in its Latest Earnings Report.
Buisiness Insider. Retrieved from https://www.businessinsider.com/google-stock-buy- back-8589869056-perfect-number-2018-2 |
| The Great Internet Mersenne Prime Search | The Mathcast. (2008, Nov. 5). The Great Internet Mersenne Prime Search [mp3].
Retrieved from http://mathfactor.uark.edu/2008/11/er-the-great-internet-mersenne-prime-search/ |
| Polygon, Prime and Perfect Numbers | Griffin, H. (2015). Polygon, Prime, and Perfect Numbers. Retrieved from
https://slideplayer.com/slide/5277563/ |
| Factor Trees | (N.d.). Factor Trees. Math Playground. Retrieved from
https://www.mathplayground.com/factortrees.html |
| Prime Factorization Calculator | (N.d.). Prime Factorization Calculator. Math Warehouse. Retrieved from
http://www.mathwarehouse.com/arithmetic/numbers/prime-number/prime-factorization-calculator.php |
| Number Ninja | (N.d.). Prime Numbers. ABCYa. Retrieved from
http://www.abcya.com/number_ninja_factors.htm |
| Perfect Number Calculator | (N.d). Perfect Number Calculator. BYJU's: The Learning App.
Retrieved from https://byjus.com/perfect-number-calculator/ |
| What is a Perfect Number? | Osborn, K. (N.d.). What is a Perfect Number?. Retrieved from
https://study.com/academy/lesson/perfect-numbers-definition-formula-examples.html |
| Off the Number Line: Odd Perfect Number | Peterson, M., Huang, J. (2015). Off the Number Line: Odd Perfect Number. Mind Research Institute.
Retrieved from https://blog.mindresearch.org/blog/off-the-number-line-odd-perfect-number |
| Illustration of the Perfect Number | Wikipedia. “Illustration of the Perfect Number.”
Wikipedia, 2018. Retrieved from, https://en.wikipedia.org/wiki/Perfect_number. |