# Some of My Preprints (Not Necessarily the Published Version)

**Newton polygons and the Prouhet-Tarry-Escott problem
**, with **Maria Markovich**, submitted.
[pdf]

**Further irreducibility criteria for polynomials with non-negative coefficients
**, with **Morgan Cole** and **Scott Dunn**,
*Acta Arith.*, to appear.
[pdf]

**On the irreducibility of a polynomial associated with the Strong Factorial Conjecture
**, with **Brady Rock**,
*Colloquium Mathematicum*, to appear.
[pdf]

**Starting with gaps between k-free numbers
**, with **Sid Graham** and **Ognian Trifonov**,
*International Journal of Number Theory* 11 (2015), 1411-1435.
[pdf]

**Colorings of Pythagorean triples within colorings of the positive integers
**, with **Joshua Cooper**, **Joshua Harrington** and **Daniel White**,
*Journal of Combinatorics and Number Theory* 6 (2014), 1-16.
[pdf]

**Is every polynomial with integer coefficients near an irreducible polynomial?
**,
*Elemente der Mathematik* 69 (2014), 130-143.
[pdf]

**49598666989151226098104244512918
**, with **Sam Gross**,
*Journal of Number Theory* 137 (2014), 16-49.
[pdf]

**The non-cyclotomic part of f(x) x^n + g(x) and roots of reciprocal polynomials off the unit circle
**, with **Edward Dobrowolski** and **Andrew Vincent**,
*International Journal of Number Theory* 9 (2013), 1865-1877.
[pdf]

**On classifying Laguerre polynomials which have Galois group the alternating group
**, with **Pradipto Banerjee**, **Carrie E. Finch** and **J Russell Leidy**,
*Journal de Theorie des Nombres de Bordeaux* 25 (2013), 1-30.
[pdf]

**A polynomial investigation inspired by work of Schinzel and Sierpinski
**, with **Joshua Harrington**,
*Acta Arith.* 155 (2012), 149-161.
[pdf]

**Solving n(n+d)...(n+(k-1)d) = b y^2 with P(b) <= Ck
**, with **Shanta Laishram** and **N. Saradha**,
*International Journal of Number Theory* 8 (2012), 161-173..
[pdf]

**The distance to an irreducible polynomial, II
**, with **Michael Mossinghoff**,
*Math. Comp.* 81 (2012), 1571-1585.
[pdf]

**Laguerre polynomials with Galois group A_m for each m
**, with **Travis Kidd** and **Ognian Trifonov**,
*Journal of Number Theory* 132 (2012), 776-805.
[pdf]

**Composites that remain composite after changing a digit
**, **Mark Kozek**, **Charles Nicol** and **John Selfridge**,
*Journal of Combinatorics and Number Theory* 2 (2011), 25-36.
[pdf]

**On a polynomial conjecture of Pal Turan
**, with **Pradipto Banerjee**,
*Acta Arithmetica* 143 (2010), 239--255.
[pdf]

**On values of d(n!)/m!, phi(n!)/m! and sigma(n!)/m!
**, with **Dan Baczkowski**, **Florian Luca** and **Ognian Trifonov**,
*International Journal of Number Theory* 6 (2010), 1199-1214.
[pdf]

**On the factorization of consecutive integers
**, with **Michael Bennett** and **Ognian Trifonov**,
*Journal fur die reine und angewandte Mathematik (Crelle)* 629 (2009), 171-200.
[pdf]

**Yet another generalization of the Ramanujan-Nagell equation
**, with **Michael Bennett** and **Ognian Trifonov**,
*Acta Arithmetica* 134 (2008), 211-217.
[pdf]

**On powers associated with Sierpinski numbers, Riesel numbers and Polignac's conjecture
**, with **Carrie Finch** and **Mark Kozek**,
*Journal of Number Theory* 128 (2008), 1916-1940.
[pdf]
[data]

**Irreducibility and greatest common divisor algorithms for sparse polynomials
**, with **Andrew Granville** and **Andrzej Schinzel**,
Number Theory and Polynomials (ed. James McKee and Chris Smyth), LMS Lecture Note Series 352,
Cambridge Univ. Press, 2008, pp. 155-176.
[pdf]

**T. N. Shorey's influence in the theory of irreducible polynomials
**, with **Carrie Finch** and **J Russell Leidy**,
Diophantine Equations (ed. N. Saradha), Narosa Publ. House, New Delhi, 2008, pp. 77-102.
[pdf]

**Galois groups of polynomials arising from circulant matrices
**, with **Florian Luca**, **Pante Stanica** and **Robert Underwood**,
*Journal of Number Theory* 128 (2008), 59-70.
[pdf]

**Sieving by large integers and covering systems of congruences
**, with **Kevin Ford**, **Sergei Konyagin**, **Carl Pomerance** and **Gang Yu**,
*Journal of the American Mathematical Society* 20 (2007), 495-517.
[pdf]

**On the irreducibility of a truncated binomial expansion
**, with **Angel Kumchev** and **Dmitrii Pasechnik**,
*Rocky Mountain Journal of Math.* 37 (2007), 455-464.
[pdf]

**Two Diophantine approaches to the irreducibility of certain trinomials
**, with **Florian Luca**, **Pante Stanica** and **Robert Underwood**,
*Acta Arithmetica* 128 (2007), 149-156.
[pdf]

**On three questions concerning 0,1-polynomials
**, with **Carrie Finch** and **Charles Nicol**,
*Journal de Theorie des Nombres de Bordeaux* 118 (2006), 357-370.
[pdf]

**Irreducibility testing of lacunary 0,1-polynomials
**, with **Douglas Meade**,
*Journal of Algorithms* 55 (2005), 21-28.
[pdf]

**A generalization of a third irreducibility theorem of I. Schur
**, with **Martha Allen**,
*Acta Arith.* 114 (2004), 183-197.
[pdf]

**On the irreducibility of 0,1-polynomials of the form f(x) x^n + g(x)
**, with **Manton Matthews, Jr.**,
*Colloq. Math.* 99 (2004), 1-5.
[pdf]

**On testing the divisibility of lacunary polynomials by cyclotomic polynomials
**, with **Andrzej Schinzel**,
*Math. Comp.* 73 (2004), 957-965.
[pdf]

**A generalization of a second irreducibility theorem of I.Schur
**, with **Martha Allen**,
*Acta Arith.* 109 (2003), 65-79.
[pdf]

**On the irreducibility of a certain class of Laguerre polynomials
**, with **Richard Williams**,
*J. Number Theory* 100 (2003), 229-250.
[pdf]

**On coverings of the integers associated with an irreducibility theorem
of A. Schinzel**.
Number theory for the millennium, II (Urbana, IL, 2000), A K Peters, Natick, MA, 2002, 1-24.
[pdf]

**On the irreducibility of the generalized Laguerre polynomials**,
with **Tsit-Yuen Lam**,
*Acta Arith.* 105 (2002), 177-182.
[pdf]

**The irreducibility of the Bessel polynomials**,
with **Ognian Trifonov**,
*J. Reine Angew. Math.* 550 (2002), 125-140.
[pdf]

**A distribution problem for powerfree values of irreducible
polynomials**,
with **Brian Beasley**,
*Periodica Math. Hungarica * 42 (2001), 123-144.
[pdf]

**On an irreducibility theorem of A. Schinzel associated with coverings
of the integers**,
with **Kevin Ford** and **Sergei Konyagin**,
*Illinois J. Math.* 44 (2000), 633-643.
[pdf]

**Classes of polynomials having only one non-cyclotomic irreducible
factor**,
with **Alexander Borisov**, **Tsit-Yuen Lam**, and **Ognian
Trifonov**, *Acta Arith.*, **90** (1999), 121-153.
[pdf]

**On the factorization of polynomials with small Euclidean norm
**,
Number theory in progress, Vol.~1 (Zakopane-Ko\'scielisko, 1997),
de Gruyter, Berlin, 1999, 143-163.
[pdf]

**An extension of a theorem of Ljunggren
**,
with **Ikhalfani Solan**,
*Math. Scand.*, 84 (1999), 5-10.
[pdf]

**On a limit point associated with the abc-conjecture**,
with **Sergei Konyagin**,
*Colloquium Mathematicum*, 76 (1998), 265-268.
[pdf]

**Norms of factors of polynomials
**, with
**Ikhalfani Solan**,
*Acta Arith.,
* 82 (1997), 243-255.
[pdf]

**Squarefree values of polynomials and the abc-conjecture**,
with **Jerzy Browkin**, **George Greaves**, and
**Andrzej Schinzel**,
*Sieve Methods, Exponential Sums, and their Applications in Number
Theory*, edited by G. Greaves, G. Harman, and M. Huxley,
Cambridge Univ. Press, 1997, pp. 65-85.
[pdf]

**The distribution of fractional parts with applications to gap results in number theory**,
with **Ognian Trifonov**,
*Proc. London Math. Soc.* (3) 73 (1996), 241-278.
[pdf]

**A generalization of an irreducibility theorem of I. Schur**,
*Analytic Number Theory: Proceedings of a Conference in Honor of Heini
Halberstam, Volume 1*, edited by B.C. Berndt, H.G. Diamond, and
A.J. Hildebrand, Birkhauser, Boston, 1996, 371-396.
[pdf]

**Squarefree values of polynomials all of whose coefficients are 0 and
1**,
with **Sergei Konyagin**, *Acta Arith.*, 74 (1996), 191-205.
[pdf]

**The irreducibility of all but finitely many Bessel polynomials**,
*Acta Math.*, 174 (1995), 383-397.
[pdf]

**The distribution of squarefull numbers in short intervals**,
with **Ognian Trifonov**,
*Acta Arith.*, 67 (1994), 323-333.
[pdf]

**Powerfree values of binary forms**,
*Journal of Number Theory*, 49 (1994), 250-268.
[pdf]

**The minimal Euclidean norm of an algebraic number is effectively
computable**,
with **Michael Robinson** and **Ferrell Wheeler**,
*Journal of Algorithms*, 16 (1994), 309-333.
[pdf]

**On the distribution of gaps between squarefree numbers**,
*Mathematika*, 40 (1993), 88-101.
[pdf]

**A result on the digits of a^n**,
with **Richard Blecksmith** and **Charles Nicol**,
*Acta Arith.*, 64 (1993), 331--339.
[pdf]

**Short interval results for k-free values of irreducible
polynomials**,
*Acta Arith.*, 64 (1993), 249--270.
[pdf]

**An estimate for the
number of reducible Bessel Polynomials of bounded degree**,
with **Sid Graham**,
*Colloquium Mathematicum*, 65 (1993), 65-68.
[pdf]

**Squarefree values of polynomials**,
*Acta Arith.*, 60 (1992), 213-231.
[pdf]

**On gaps between squarefree numbers II**,
with **Ognian Trifonov**,
*Journal of the London Math. Soc. (2)*, 45 (1992), 215-221.
[pdf]