# Enrique Treviño ### Associate Professor of Mathematics

#### Areas of Specialization

Analytic Number Theory
Computational Number Theory

#### Education

PhD Dartmouth College 2011
Thesis: Numerically Explicit Estimates for Character Sums

MA Dartmouth College
BA University of Texas at El Paso

Selected Courses Taught

MATH 499: Great Theorems in Mathematics (Senior Seminar)
MATH 491: Tutorial (Topology)
MATH 411: Real Analysis II
MATH 375: Combinatorics
MATH 340: Geometry
MATH 331: Modern Algebra II
MATH 330: Modern Algebra I
MATH 329: Number Theory
MATH/CS 323: Cryptography
MATH 311: Real Analysis I
MATH 230: Abstract and Discrete Mathematics
MATH 214: Differential Equations
MATH 210: Multivariable Calculus
MATH 160: Math Methods and Applications
MATH 150: Introduction to Probability and Statistics
MATH 110: Calculus I
MATH 109: Calculus 1b
MATH 108: Calculus 1a
CS 112: Introduction to Programming
FIYS 169: Recreational Mathematics
MATH 53 (Swarthmore College): Analytic Number Theory
MATH 77 (Swarthmore College): Algebraic Number Theory
MATH 27 (Swarthmore College): Linear Algebra
MATH 25 (Swarthmore College): Calculus II
MATH 20 (Dartmouth College): Discrete Probability

Selected Honors

Travel grant from the American Mathematical Society to attend the 1st Congress of the Americas held in Guanajuato in August 2013.

Swarthmore College Research Award (2011-2013)

GAANN Fellowship (2006-2007)

Top 200 in the 66th Putnam exam, Dec. 2005

Publications
##### Books

Cuban Mathematical Olympiads. Written by Robert Bosch. Translated by Enrique Treviño. Published by XYZ Press (2017). ISBN: 978-0-9968745-4-0

##### Articles

18. On generalizing happy numbers to fractional base number systems (with M. Zhylinski*).
Involve vol. 12 (2019), no. 7, pp. 1143-1151.
17. Probabilistic Proof that 1+2+…+n = n(n+1)/2.
American Mathematical Monthly vol. 126 (2019), no. 9, p. 840
16. A birthday in St. Petersburg.
The College Mathematics Journal vol. 50 (2019), no. 1, pp. 36-40.
15. An Inclusion-Exclusion Proof of Wilson’s Theorem.
The College Mathematics Journal vol. 49 (2018), no. 5, pp. 367-368.
14. Walking on rational numbers and a self-referential formula
with M. Fortman*, K. Kupiec*, and M. Rawlings*. Elemente der Mathematik 73 (2018), no.4, 161-169.
13. A short proof of a sum of powers formula
American Mathematical Monthly 125 (2018), no. 7, 659-659.
12. Finding the four squares in Lagrange’s Theorem (with Paul Pollack). Integers 18A (2018), article A15, 16 pages (electronic).
11. Counting Perfect Polynomials
(with U.C. Cengiz and P. Pollack). Finite Fields and Their Applications 47C (2017) pp. 242-255 DOI information: 10.1016/j.ffa.2017.05.006.
10. Resolving Grosswald’s conjecture on GRH (with K. McGown and T. Trudgian) Functiones et Approximatio, Commentarii Mathematici 55.2 (2016), pp. 215-225.
9. The Burgess inequality and the least k-th power non-residue International Journal of Number Theory Vol. 11, No. 5 (2015), pp. 1-26.
8. The smoothed Pólya-Vinogradov inequality (with K. Adamczewski), Integers 15 (2015), 11 pages (electronic).
7. The least k-th power non residue Journal of Number Theory  149 (2015), pp. 201-224. DOI information: 10.1016/j.jnt.2014.10.019
6. The primes that Euclid forgot (with P. Pollack), American Mathematical Monthly 121 (2014), no. 5, 433-437.
5. Sets of monotonicity for Euler’s totient function (with P. Pollack and C. Pomerance), The Ramanujan Journal 30 (2013), no. 3, 379-398.
4. On the maximum number of consecutive integers on which a character is constant Moscow Journal of Combinatorics and Number Theory (2012), vol.2, iss. 1, pp. 56-72.  Corrigendum appeared in Moscow Journal of Combinatorics and Number Theory (2017), vol.7, iss. 3.
3. The least inert prime in a real quadratic field, Mathematics of Computation, vol. 81, no. 279, July 2012, pp. 1777-1797.
2. Multi-dimensional Frobenius problem (with J. Amos, I. Pascu, V. Ponomarenko and Y. Zhang), Involve, a Journal of Mathematics 4-2 (2011), 187—197.
1. On the counting function for the generalized Niven numbers (with R. Daileda, J. Jou, R. Lemke-Oliver and E. Rossolimo), J. Théor. Nombres Bordeaux 21 (2009), no. 3, 503—515.

Articles Accepted for Publications

1. Egyptian fractions of length 3 (with C. Banderier, C. A. Gómez Ruiz, F. Luca, and F. Pappalardi).
To Appear in Revista de la Unión Matemática Argentina.

2. The least quadratic non-residue (with K. McGown).
To Appear in Contributions of Mexican mathematicians abroad in pure and applied mathematics. Fourth Meeting Matemáticas Mexicanos en el Mundo.

3. On sums of consecutive triangular numbers (with P. Pollack and D. Subramaniam*).
To Appear in Integers.

4. Expected number of dice rolls for the sum to reach n.
To Appear in American Mathematical Monthly.

The Fundamental Theorem of Algebra by William Braubach, Fall 2016.
Transcendental Numbers by Jacob Juillerat, Spring 2016.

Richter Projects Supervised

What’s so rational about the alphabet? by Kevin Kupiec and Marina Rawlings, Summer 2014 (3-week project).
Finding perfect polynomials mod 2 by Ugur Caner Cengiz, Summer 2014 (10-week project).
On Tupper’s Self-Referential Formula by Margaret Fortman, Summer 2015 (4-week project).
First-world solutions to First-year problems by Robert Mecham, Summer 2015 (10-week project).
Beatty Sequences and the Prime Race by Noel Orwothwun, Summer 2016 (4-week project).