PAPERS
- with Nathan Jones and Peter Stevenhagen:
Locally Imprimitive Points on Elliptic Curves. to appear. 
-  with Herish Abdullah and Andam Ali Mustafa:
Divisibility of reduction in groups of rational numbers II.
Int. J. Number Theory 19 (2023), no. 2, 247–260. *
-  with Herish Abdullah and Andam Ali Mustafa:
 Density of the quasi r-rank Artin problem.
Funct. Approx. Comment. Math. 65 (2021), no. 1, 73–93.*
-  Cyril Banderier, Carlos Alexis Gómez Ruiz,Florian Luca and Treviño, Enrique:
On Egyptian fractions of length 3.
Rev. Un. Mat. Argentina 62 (2021), no. 1, 257–274.  * 
-  with Florian Luca:
On the number of divisors of the least common multiples of shifted prime powers.
Funct. Approx. Comment. Math. 64 (2021), no. 2, 153–161.*
-  with Florian Luca:
On ternary Egyptian fractions with prime denominator.
Res. Number Theory 5 (2019), no. 4, Paper No. 34, 14 pp.*
-  with Min Sha, Igor E. Shparlinski and Cameron L. Stewart:
On multiplicatively dependent vectors of algebraic numbers. Trans. 
Amer. Math. Soc. 370 (2018), no. 9, 6221-6244.*
-  with Kalyan Chakraborty and Jorge Jimènez Urroz: Pairs of integers which are mutually squares.  Sci. China Math. 60 (2017), no. 9, 1633-1646.*
-  with M. Anwar: On simultaneous primitive roots. Acta Arith. 180 (2017), no. 1, 35-43.
*
- with A. Susa: An analogue to Artin's conjecture for multiplicative subgroups of the 
rationals. Arch. Math. 101 (2013), 319-330  *
-  Divisibility of reduction in groups of rational numbers Math. Comp. 84 (2015), 385-407
 *
-  On the exponents of the group of points of an Elliptic curve over a finite field. Proc. Amer. 
Math. Soc. 139 No. 7
  (2011) 2337-2341. *
-  with W. Banks and 
  I. Shparlinski:  Possible Group Structures of Elliptic Curves over Finite Fields. Experimental 
Mathematics 21, Issue 1, March 2012, pages 11-25. *
-  with  Étienne Fouvry, F. 
Luca and  
  I. Shparlinski: 
Counting dihedral and quaternionic extensions. Trans. Amer. Math. Soc. 363 No. 6
  (2011) 3233-3253. *
-  with S. D. Adhikari, 
R. Balasubramanian and P. Rath: Some zero-sum 
constants with weights. 
Proceedings of Indian Academy of Sciences. 118, No. 2, (2008), 183-188.
*
-  with F. Luca:
Composite positive integers with an average prime factor. Acta Arithmetica 
129 (2007), 197-201
* 
  
-  with  Arto Lepistö and 
Kalle Saari: 
Transposition Invariant Words. Theoretical Computer Science 380, Issue 3  (June 2007) 
377-387, Combinatorics on words. *
-  with A. Glibichuk and F. Luca:
  On the equation t(l(n))=w(n)+k. Michigan Mathamatical Journal
55, Issue 3  (2007), 671-692. 
 *  
-  with A. Susa: On a problem of Schinzel and 
Wójcik involving equalities
between multiplicative orders. Math. Proc. Cambridge Philos. Soc. 
146.2 (2009), 303-319. *
  
-  with W. Banks,  K. Ford,
  F. Luca and 
  I. Shparlinski: Values of the
Euler Function in Various
Sequences. Monats. Math.
  146 (2005), 1-19. *
  
-  with W. Banks, J. B. Friedlander,
  F. Luca and 
  I. Shparlinski: Coincidences in the Values of the Euler and Carmichael 
Functions. Acta Arithmetica 122.3 (2006), 207-234. *
  
-  with Alf
van der Poorten: 
Pseudo-Elliptic Integrals, Units and Torsion.
J. Aust. Math. Soc. 79 
(2005), 335-347. *
  
-  A survey on k-power freeness. Proceeding of
the Conference in Analytic Number Theory in Honor of Prof. Subbarao at I.M.Sc. Chennai, January 2003.
 Number theory, 71--88, Ramanujan Math. Soc. Lect. Notes Ser. 1, 
Ramanujan Math. Soc.,
   Mysore, 2005.
*
  
-  with W.
Banks: Powerfree Values of the Euler Function. J. Num. Theory
120 (2006) 326-348.
*
  
-  with F.
Luca: Members of binary recurrences on lines of the Pascal
triangle. Publ.
Math. Debrecen 67 1-2 (2005) 103-113. *
-  with S. das Adhikari, Y. G. Chen, J. B. Friedlander, S. Konyagin: Contributions to zero-sum problems. Discrete Math 306 (2006), 1-10. 
*
- with S.
  Konyagin: Enumerating permutation polynomials over finite
fields by degree II. Finite Fields and their Applications
12 (2006) 26-37. *
  
- Squarefree Values of the Order Function.
  New York Journal of Mathematics 9 (2003), 331-344. *
  
- with F.
Saidak and 
  I. Shparlinski: Squarefree
Values of the Carmichael Function.
  J. Num.
  Theory 103 (2003) 122-131. *
  
- with D. Cosentino: Fast computation of
  k-dimensional residues and an application to probabilistic
  encryption.  *
  
- with C.
  David: Average Frobenius Distribution for inerts in
  Q(i).
  Journal
of the Ramanujan Mathematical Society 19 (2004, no 3), 1-21. *
  
- with C. Malvenuto: 
 Enumerating
  Permutation Polynomials II: k-cycles with minimal degree. Finite Fields and their
  Applications 10 (2004) 62-76. *
- with S. das Adhikari: On the
  visibility problem in the function field case.
  C. R. Math. Acad. Sci. Soc. R. Can.
  24 (2002), no. 3, 109-116.
  *
- with S.
  Konyagin: 
  Enumerating Permutation Polynomials over finite fields by degree. 
  Finite Fields and their
  Applications 8 (2002) 548-553. *
  
- with C. Malvenuto: 
Enumerating
  Permutation Polynomials I: Permutations with non maximal
degree. Finite Fields and their
  Applications 8 (2002) 531-547. * - corrigendum ibid.
13 1 (2007) 171-174. *
  
- with B. Mans and I. Shparlinski: On the spectral
 Adams property for circulant graphs. Discrete
Math. 254
(2002) 309-329. * 
- with E. Croot, D. E.
Dobbs, J. B.
Friedlander, A. J.
  Hetzel: Binary
  Egyptian Fractions. J. Num.
  Theory 84 (2000) 63-79. *
  
- with L. Cangelmi: On the
  r-rank Artin Conjecture II. J. Num. Theory 75 No.1
  (1999) 120-132. *  
- with C. David and H. Kisileveski:
  
  Galois representations with non surjective traces. Canad. J. Math.
  51 No. 5 (1999) 936-951. *
  
- with C. David: Average
  Frobenius Distribution of Elliptic Curves. Internat. Math. Res. Notices
  4
  (1999) 165-183. *
- On
  Hooley's Theorem with weights. Rend. Sem. Mat. Polit.
  Univ. Torino 53 No. 4 (1995) 375-388. *
  
- with J. von zur
  Gathen: Density Estimates related to Gauss periods. Lam, Kwok-Yan
  (ed.) et al., 
Cryptography and computational number theory.
Proceedings of the
  workshop, CCNT'99, Singapore, November 22-26, 1999. Basel: Birkhäuser.
Prog. Comput. Sci. Appl.
  Log. 20, 33-41 (2001). *
  
- The
  r-rank Artin Conjecture. Math.
  Comp. 66 (1997) 853-868. *
  
- On the
  order of finitely generated subgroups of Q* and
  divisors of p-1. J.
  Num. Theory 57 No. 2 (1996) 207-222. *
  
- with I. Shparlinski: The Artin
  Conjecture for function fields. Finite Fields and their
  Applications 1 (1995) 399-404. *
  
- with H. Kisilevsky:
  
 On the exponent of the ideal class group of function fields. Acta Arithmetica
  LXXII No. 4 (1995) 311-321. *
  
- 
  
  On minimal sets of generators for primitive
  roots. Bull. Canad. Math.
  Soc. 38 No. 4 (1995) 465-468. *
  
- On the exponent of the ideal class group of
   Q(Ö
-d). Proc. Amer. Math. Soc. 123 No. 3
  (1995) 663-671. *
  
- with H. E. Campbell, I. Hughes and
  P. Selik: On
  The ring of Invariants of F*2n. Comment. Math.
  Helvetici 66 (1991) 322-331. *
OTHER PUBLICATIONS
- Editor: with Alina Carmen Cojocaru and Chantal David:
Scholar A Scientific Celebration Highlighting Open Lines of Arithmetic Research
 Conference in Honour of M. Ram Murty’s Mathematical Legacy on His 60th Birthday.
  Contemporary Mathematics
Centre de Recherches Mathématiques Proceedings
Volume: 655 (2015) 256 pp 
 
- Editor: with F. Dramis, A. Gambacorta, R. Mignani and A. Trentalance
   Stato della Ricerca e sviluppi futuri: I primi dieci anni di
attività della Facoltà M.F.N. di Roma Tre. Atti della Conferenza -
Novembre 2001.
- Note di crittografia a chiave
  pubblica. 
  - Vol 1. Number Theoretic background
  
- Vol 2. RSA, factoring a primality In preparation.
 
- Book Review: with P. Mihailescu: Review
  of the book "Elliptic Curves in
  Cryptography" by I. Blake, G. Seroussi, N. Smart. Math. Comp. 2001. *
- with C. Malvenuto: 
On the Enumeration of Permutation Polynomials. Proc of Colloque
LaCIM 2000 Combinatoire,
  Informatique et Applications Laboratoire de Combinatoire et d'Informatique
  Mathématique (LaCIM) Université du
  Québec à Montréal, 7 au 10 septembre 2000. *
- with B. Mans and I. Shparlinski: On
Adams
  Conjecture for circulant graphs Hsu, Wen-Lian (ed.) et al.,
Computing and
  combinatorics. 4th annual international conference, COCOON '98,
  Taipei, Taiwan, ROC, August 12-14, 1998. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci.
  1449, 251-260 (1998). *
- Editor: with A. Perelli and C. Viola: Atti
  del Primo incontro Italiano di Teoria dei Numeri, Rend. Sem. Mat. Pol. Univ.
  Torino 53 No. 3-4 (1995).
- L'esponente del gruppo delle classi in campi
  di funzioni. Estratti Convegno Giornate di Geometria Algebrica ed
  argomenti Correlati III, L'Aquila 1995.
- PhD Thesis: 
Remarks on Artin Conjecture on Primitive Roots, McGill
  University, Montreal 1992.  *