References E.7 Useful Articles
[1]
Ivan Niven and Barry Powell, Primes in Certain Arithmetic Progressions, The American Mathematical Monthly, June-July 1976, 83 no. 6, 467β469.
[2]
D. Zagier, A One-Sentence Proof That Every Prime pβ‘1( mod 4) Is a Sum of Two Squares, The American Mathematical Monthly, February 1990, 97 no. 2, 144β144.
[3]
Andrew Granville and Greg Martin, Prime Number Races, The American Mathematical Monthly, January 2006, 113 no. 1, 1β33.
[4]
David A. Cox, Why Eisenstein Proved the Eisenstein Criterion and Why SchΓΆnemann Discovered It First, The American Mathematical Monthly, January 2011, 118 no. 1, 3β21.
[5]
Steven H. Weintraub, On Legendreβs Work on the Law of Quadratic Reciprocity, The American Mathematical Monthly, March 2011, 118 no. 3, 210β216.
[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, 822β831.
[7]
Xianzu Lin, Infinitely Many Primes in the Arithmetic Progression knβ1, The American Mathematical Monthly, January 2015, 122 no. 1, 48β51.
[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, 29β34.
[9]
Roger B. Nelsen, Proof Without Words: Square Triangular Numbers and Almost Isosceles Pythagorean Triples, College Mathematics Journal, May 2016, 47 no. 3, 179β179.
[10]
David Lowry-Duda, Unexpected Conjectures about -5 Modulo Primes, College Mathematics Journal, January 2015, 46 no. 1, 56β57.
[11]
William G. Stanton and Judy A. Holdener, Abundancy βOutlawsβ of the Form Ο(N)+tN, Journal of Integer Sequences, 10
[12]
D. R. Slavitt, Give Way To God, or The Dying Christ β Pierre de Fermat, The Mathematical Intelligencer, Summer 2012, 34 no. 2, 3β5.
[13]
Paul Nahin, The Mysterious Mr. Graham, The Mathematical Intelligencer, Spring 2016, 38 no. 1, 48β51.
[14]
P. A. Weiner, The abundancy index, a measure of perfection, Mathematics Magazine, October 2000, 73 no. 4, 307β310.
[15]
Andrew Bremner, Positively prodigious powers or how Dudeney done it?, Mathematics Magazine, April 2011, 84 no. 2, 120β125.
[16]
Rafael Jakimczuk, The Quadratic Character of 2, Mathematics Magazine, April 2011, 84 no. 2, 126β127.
[17]
Russell A. Gordon, Properties of Eisenstein Triples, Mathematics Magazine, February 2012, 85 no. 1, 12β25.
[18]
Roger B. Nelsen, Proof Without Words: Infinitely Many Almost-Isosceles Pythagorean Triples Exist, Mathematics Magazine, April 2016, 89 no. 2, 103β104.
[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, 65β74.
[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, 562β564.
[22]
F. Saidak, A new proof of Euclid's theorem, The American Mathematical Monthly, December 2006, 113 no. 10, 937β938.
[23]
Yannick Saouter and Patrick Demichel, A sharp region where Ο(x)βli(x) is positive, Mathematics of Computation, October 2010, 79 no. 272, 2395β2405.
[24]
Kent Boklan and John Conway, Expect at Most One Billionth of a New Fermat Prime!, The Mathematical Intelligencer, 2017, 39 no. 1, 3β5.
[25]
Bruce Berndt et al., The Circle Problem of Gauss and the Divisor Problem of DirichletβStill Unsolved, The American Mathematical Monthly, February 2018, 125 no. 2, 99β114.
[26]
William Dunham, The Early (and Peculiar) History of the MΓΆbius Function, Mathematics Magazine, April 2018, 91 no. 2, 83β91.
[27]
Enrique TreviΓ±o, An Inclusion-Exclusion Proof of Wilson's Theorem, The College Mathematics Journal, November 2018, 49 no. 6, 367β377.
[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, 22β27.
[30]
John Brillhart, A Note on Euler's Factoring Problem, The American Mathematical Monthly, December 2009, 116 no. 10, 928β931.
[31]
Christian Aebi and Grant Cairns, Sums of Quadratic Residues and Nonresidues, The American Mathematical Monthly, February 2017, 124 no. 2, 166β169.
[32]
A. Rotkiewicz and K. Ziemak, On Even Pseudoprimes, The Fibonacci Quarterly, May 1995, 33 no. 2, 123β125.
[33]
Lars-Daniel Γhman, Are Induction and Well-Ordering Equivalent, The Mathematical Intelligencer, September 2019, 41 no. 3, 33β40.
[34]
Trevor Woolsey, A Superpowered Euclidean Prime Generator, The American Mathematical Monthly, April 2017, 124 no. 4, 351β352.
[35]
Edray Goins et al., Lattice Point Visibility on Generalized Lines of Sight, The American Mathematical Monthly, August-September 2018, 125 no. 7, 593β601.
[36]
Dylan Fridman et al., A Prime-Representing Constant, The American Mathematical Monthly, January 2019, 126 no. 1, 70β73.
[37]
Roger Nelsen, Even Perfect Numbers End in 6 or 28, Mathematics Magazine, April 2018, 91 no. 2, 140β141.
[38]
Howard Sporn, Pythagorean Triples, Complex Numbers, and Perplex Numbers, The College Mathematics Journal, March 2017, 48, no. 2, 115β122.
[39]
Aalok Thakkar, Infinitude of Primes Using Formal Languages, The American Mathematical Monthly, October 2018, 125, no. 8, 745β749.
[40]
Hing-Lun Chan and Michael Norrish, A String of Pearls: Proofs of Fermat's Little Theorem in βHawblitzel C., Miller D. (eds.) Certified Programs and Proofs, CPP 2012β, Lecture Notes in Computer Science, 7679, 188β207.
[41]
Solomon Golomb, Combinatorial Proof of Fermat's βLittleβ Theorem, The American Mathematical Monthly, December 1956, 63, no. 10, 718.
[42]
Enrique TreviΓ±o, An Inclusion-Exclusion Proof of Wilson's Theorem, The College Mathematics Journal, November 2018, 49, no. 5, 367β368.