[1]
Ivan Niven and Barry Powell, Primes in Certain Arithmetic Progressions, The American Mathematical Monthly, June-July 1976, 83 no. 6, 467–469.
References E.7 Useful Articles
Throughout the text, I’ve attempted to reference articles in so-called ‘generalist’ mathematics publications which have been useful or intriguing. See also the collection [E.6.4], where some of these appear.
[2]
D. Zagier, A One-Sentence Proof That Every Prime \(p\equiv 1 (\text{ mod }4)\) Is a Sum of Two Squares, The American Mathematical Monthly, February 1990, 97 no. 2, 144–144.
[3]
Andrew Granville and Greg Martin, Prime Number Races, The American Mathematical Monthly, January 2006, 113 no. 1, 1–33.
[4]
David A. Cox, Why Eisenstein Proved the Eisenstein Criterion and Why Schönemann Discovered It First, The American Mathematical Monthly, January 2011, 118 no. 1, 3–21.
[5]
Steven H. Weintraub, On Legendre’s Work on the Law of Quadratic Reciprocity, The American Mathematical Monthly, March 2011, 118 no. 3, 210–216.
[6]
Jonathan Bayless and Dominic Klyve, Reciprocal Sums as a Knowledge Metric: Theory, Computation, and Perfect Numbers, The American Mathematical Monthly, November 2013, 120 no. 9, 822–831.
[7]
Xianzu Lin, Infinitely Many Primes in the Arithmetic Progression \(kn-1\), The American Mathematical Monthly, January 2015, 122 no. 1, 48–51.
[8]
Reinhard Laubenbacher and David Pengelley, Eisenstein’s Misunderstood Geometric Proof of the Quadratic Reciprocity Theorem, The College Mathematics Journal, January 1994, 25 no. 1, 29–34.
[9]
Roger B. Nelsen, Proof Without Words: Square Triangular Numbers and Almost Isosceles Pythagorean Triples, College Mathematics Journal, May 2016, 47 no. 3, 179–179.
[10]
David Lowry-Duda, Unexpected Conjectures about -5 Modulo Primes, College Mathematics Journal, January 2015, 46 no. 1, 56–57.
[11]
William G. Stanton and Judy A. Holdener, Abundancy “Outlaws” of the Form \(\frac{\sigma(N)+t}{N}\), Journal of Integer Sequences, 10
[12]
D. R. Slavitt, Give Way To God, or The Dying Christ – Pierre de Fermat, The Mathematical Intelligencer, Summer 2012, 34 no. 2, 3–5.
[13]
Paul Nahin, The Mysterious Mr. Graham, The Mathematical Intelligencer, Spring 2016, 38 no. 1, 48–51.
[14]
P. A. Weiner, The abundancy index, a measure of perfection, Mathematics Magazine, October 2000, 73 no. 4, 307–310.
[15]
Andrew Bremner, Positively prodigious powers or how Dudeney done it?, Mathematics Magazine, April 2011, 84 no. 2, 120–125.
[16]
Rafael Jakimczuk, The Quadratic Character of 2, Mathematics Magazine, April 2011, 84 no. 2, 126–127.
[17]
Russell A. Gordon, Properties of Eisenstein Triples, Mathematics Magazine, February 2012, 85 no. 1, 12–25.
[18]
Roger B. Nelsen, Proof Without Words: Infinitely Many Almost-Isosceles Pythagorean Triples Exist, Mathematics Magazine, April 2016, 89 no. 2, 103–104.
[19]
C. Edward Sandifer, How Euler Did It: Odd Perfect Numbers, MAA Online, November 2006
[20]
Matthias Beck, How to change coins, M&M’s, or chicken nuggets: The linear Diophantine problem of Frobenius, in Resources for Teaching Discrete Mathematics: Classroom Projects, History Modules, and Articles (B. Hopkins, ed.), Mathematical Association of America, 2009, 65–74.
[21]
S. A. Rankin, The Euclidean Algorithm and the Linear Diophantine Equation \(ax + by = \gcd(a, b)\), The American Mathematical Monthly, June-July 2013, 120 no. 6, 562–564.
[22]
F. Saidak, A new proof of Euclid’s theorem, The American Mathematical Monthly, December 2006, 113 no. 10, 937–938.
[23]
Yannick Saouter and Patrick Demichel, A sharp region where \(\pi(x)-li(x)\) is positive, Mathematics of Computation, October 2010, 79 no. 272, 2395–2405.
[24]
Kent Boklan and John Conway, Expect at Most One Billionth of a New Fermat Prime!, The Mathematical Intelligencer, 2017, 39 no. 1, 3–5.
[25]
Bruce Berndt et al., The Circle Problem of Gauss and the Divisor Problem of Dirichlet—Still Unsolved, The American Mathematical Monthly, February 2018, 125 no. 2, 99–114.
[26]
William Dunham, The Early (and Peculiar) History of the Möbius Function, Mathematics Magazine, April 2018, 91 no. 2, 83–91.
[27]
Enrique Treviño, An Inclusion-Exclusion Proof of Wilson’s Theorem, The College Mathematics Journal, November 2018, 49 no. 6, 367–377.
[28]
John Cosgrave and Karl Dilcher, Extensions of the Gauss-Wilson Theorem, Integers, 2008, 8 no. 1, A39.
[29]
Ernest Eckert, The Group of Primitive Pythagorean Triangles, Mathematics Magazine, February 1984, 57 no. 1, 22–27.
[30]
John Brillhart, A Note on Euler’s Factoring Problem, The American Mathematical Monthly, December 2009, 116 no. 10, 928–931.
[31]
Christian Aebi and Grant Cairns, Sums of Quadratic Residues and Nonresidues, The American Mathematical Monthly, February 2017, 124 no. 2, 166–169.
[32]
A. Rotkiewicz and K. Ziemak, On Even Pseudoprimes, The Fibonacci Quarterly, May 1995, 33 no. 2, 123–125.
[33]
Lars-Daniel Öhman, Are Induction and Well-Ordering Equivalent?, The Mathematical Intelligencer, September 2019, 41 no. 3, 33–40.
[34]
Trevor Woolsey, A Superpowered Euclidean Prime Generator, The American Mathematical Monthly, April 2017, 124 no. 4, 351–352.
[35]
Edray Goins et al., Lattice Point Visibility on Generalized Lines of Sight, The American Mathematical Monthly, August-September 2018, 125 no. 7, 593–601.
[36]
Dylan Fridman et al., A Prime-Representing Constant, The American Mathematical Monthly, January 2019, 126 no. 1, 70–73.
[37]
Roger Nelsen, Even Perfect Numbers End in 6 or 28, Mathematics Magazine, April 2018, 91 no. 2, 140–141.
[38]
Howard Sporn, Pythagorean Triples, Complex Numbers, and Perplex Numbers, The College Mathematics Journal, March 2017, 48, no. 2, 115–122.
[39]
Aalok Thakkar, Infinitude of Primes Using Formal Languages, The American Mathematical Monthly, October 2018, 125, no. 8, 745–749.
[40]
Hing-Lun Chan and Michael Norrish, A String of Pearls: Proofs of Fermat’s Little Theorem in “Hawblitzel C., Miller D. (eds.) Certified Programs and Proofs, CPP 2012”, Lecture Notes in Computer Science, 7679, 188–207.
[41]
Solomon Golomb, Combinatorial Proof of Fermat’s “Little” Theorem, The American Mathematical Monthly, December 1956, 63, no. 10, 718.
[42]
Steven R. Benson, Pythagorean Paper Folding, Mathematics Magazine, February 2021, 94, no. 1, 34–42.
[43]
Zafer Selcuk Aygin and Kenneth S. Williams, Why does a Prime \(p\) Divide a Fermat Number?, Mathematics Magazine, October 2020, 93, no. 4, 288–294.
[44]
Shen Kangsheng, Historical Development of the Chinese Remainder Theorem, Archive for History of Exact Sciences, 1988, 38, no. 4, 285–305.
[45]
J. Sesiano, Two Problems of Number Theory in Islamic Times, Archive for History of Exact Sciences, 1991, 41, no. 3, 235–238.
[46]
David J. Hunter and Paul T. von Hippel, How Rare Is Symmetry in Musical 12-Tone Rows?, The American Mathematical Monthly, February 2003, 110, no. 2, 124–132.
