# Diego Marques

## Research

### Published Papers

#### 2016

• The solution of a version of a Mahler's question. Journal of Number Theory (Print), v. 163, p. 510-519, 2016.
• (with J. Schleischitz) On a problem posed by Mahler, Journal of the Australian Mathematical Society (2001. Online), v. 100, p. 86-107, 2016.
• (with J. Ramirez) On exceptional sets: the solutions of a problem posed by K. Mahler. Bulletin of the Australian Mathematical Society, v. 94, p. 15-19, 2016.
• (with J. Ramirez and E. Silva) A note on lacunary power series with rational coefficients. Bulletin of the Australian Mathematical Society, v. 93, p. 372-374, 2016.
• (with C. G. Moreira) On variations of the Liouville constant which are also Liouville numbers. Proceedings of the Japan Academy. Series A Mathematical Sciences, v. 92, p. 39-40, 2016.
• (with V. Facó) Tribonacci numbers and the Brocard-Ramanujan equation. Journal of Integer Sequences, v. 19, p. 16.4.4, 2016.
• (with P. Trojovsky) Terms of generalized Fibonacci sequences that are powers of their orders. Lithuanian Mathematical Journal , v. 56, p. 1-10, 2016.

#### 2015

• (with A. P. Chaves) A Diophantine equation related to the sum of powers of two consecutive generalized Fibonacci numbers. Journal of Number Theory (Print), v. 156, p. 1-14, 2015. pdf
• A new Fibonacci-Lucas relation. The American Mathematical Monthly, v. 122, p. 683, 2015. pdf
• (with P. Trojovsky) The $$p$$-adic order of some Fibonomial coefficients. Journal of Integer Sequences, v. 18, p. 15.3.1, 2015. link
• (with A. P. Chaves) Fibonacci $$s$$-Cullen and $$s$$-Woodall Numbers. Journal of Integer Sequences, v. 18, p. 15.1.4, 2015. link
• (with J. Ramirez) On transcendental analytic functions mapping an uncountable class of $$U$$-numbers into Liouville numbers. Proceedings of the Japan Academy. Series A Mathematical Sciences, v. 91, p. 25-28, 2015. link
• (with C. G. Moreira) On a question proposed by K. Mahler concerning Liouville numbers. Bulletin of the Australian Mathematical Society, v. 91, p. 29-33, 2015. pdf

#### 2014

• (with A. P. Chaves) An Explicit Family of $$U_m$$-numbers. Elemente der Mathematik, v. 69, p. 18-22, 2014. pdf
• (with P. Trojovsky) On some new identities for the Fibonomial coeficients. Mathematica Slovaca, v. 64, p. 809-818, 2014. pdf
• (with A. P. Chaves) A Diophantine equation related to the sum of squares of consecutive $$k$$-generalized Fibonacci numbers. The Fibonacci Quarterly, v. 52, p. 70-74, 2014. pdf
• On the spacing between terms of generalized Fibonacci sequences. Colloquium Mathematicum, v. 134, p. 267-280, 2014. pdf
• Generalized Fibonacci numbers of the form $$2^a + 3^b + 5^c$$. Sociedade Brasileira de Matematica. Boletim, Nova Serie, v. 45, p. 543-557, 2014. pdf
• Yet Another 'Direct' Proof of the Uncountability of the Transcendental Numbers. The American Mathematical Monthly, v. 121, p. 631, 2014. pdf
• On generalized Cullen and Woodall numbers which are also Fibonacci numbers. Journal of Integer Sequences, v. 17, p. 14.9.4, 2014. link
• (with V. Facó) Even perfect numbers among generalized Fibonacci sequences. Rendiconti del Circolo Matematico di Palermo, v. 63, p. 363-370, 2014. pdf
• (with T. Lengyel) The $$2$$-adic order of Tribonacci numbers and the equation $$T_n=m!$$. Journal of Integer Sequences, v. 17, p. 14.10.1, 2014. link
• (with F. Córes) A combinatorial proof of multiple angle formulas involving Fibonacci and Lucas numbers. Notes on Number Theory and Discrete Mathematics, v. 20, p. 35-39, 2014. link

#### 2013

• (with H. Godinho and A. Lemos) Weighted zero-sum problems over $$C_3^r$$. Algebra and Discrete Mathematics, v. 15, p. 201-212, 2013. pdf
• The proof of a conjecture concerning the intersection of $$k$$-generalized Fibonacci sequences. Bulletin Brazilian Mathematical Society (Impresso), v. 44, p. 455-468, 2013. pdf
• (with R. Garcia) A family of minimal immersed tori in $$\mathbb{S}^3$$with dense principal lines. Bulletin des Sciences Mathématiques (Paris. 1885), v. 137, p. 220-227, 2013. pdf
• (with A. Togbé) Fibonacci and Lucas numbers of the form $$2^{a}+3^{b}+5^{c}$$. Proceedings of the Japan Academy. Series A Mathematical Sciences, v. 89, p. 47-50, 2013. pdf
• Sharper upper bounds for the order of appearance in the Fibonacci sequence. The Fibonacci Quarterly, v. 51, p. 233-238, 2013. pdf
• (with J. Sellers, P. Trojovsky) On divisibility properties of certain Fibonomial coefficients by a prime $$p$$. The Fibonacci Quarterly, v. 51, p. 78-83, 2013. pdf
• The order of appearance of product of consecutive Lucas numbers. The Fibonacci Quarterly, v. 51, p. 38-43, 2013. pdf

#### 2012

• On the intersection of two distinct $$k$$-generalized Fibonacci sequences. Mathematica Bohemica, v. 137, p. 403-413, 2012. pdf
• (with A. P. Chaves and A. Togbé) On the sum of powers of terms of a linear recurrence sequence. Bulletin Brazilian Mathematical Society, v. 43, p. 397-406, 2012. pdf
• (with P. Trojovsky) On divisibility of Fibonomial coefficients by $$3$$. Journal of Integer Sequences, v. 15, p. 12.6.4, 2012. link
• (with H. Godinho and A. Togbé) On the Diophantine equation $$x^2+2^a5^b17^c=y^n$$. Communications in Mathematics, v. 20, p. 81-88, 2012. pdf
• Fibonacci numbers at most one away from the product of factorials. Notes on Number Theory and Discrete Mathematics, v. 18, p. 13-19, 2012. link
• Fixed points of the order of appearance in the Fibonacci sequence. The Fibonacci Quarterly, v. 50, p. 346-352, 2012. pdf
• The order of appearance of powers of Fibonacci and Lucas numbers. The Fibonacci Quarterly, v. 50, p. 239-245, 2012. pdf
• (with A. Togbé) On repdigits as product of consecutive Fibonacci numbers. Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, v. 44, p. 393-397, 2012. pdf
• The order of appearance of product of consecutive Fibonacci numbers. The Fibonacci Quarterly, v. 50, p. 132-139, 2012. pdf
• (with P. Trojovsky) On some new sums of Fibonomial coefficients. The Fibonacci Quarterly, v. 50, p. 155-162, 2012.
• The order of appearance of integers at most one away from Fibonacci numbers. The Fibonacci Quarterly, v. 50, p. 36-43, 2012. pdf
• (with A. Togbé) A Diophantine equation involving C-nomial coefficients. East-West Journal of Mathematics, v. 13, p. 75-79, 2012. pdf

#### 2011

• The Fibonacci version of the Brocard-Ramanujan Diophantine equation. Portugaliae Mathematica, v. 68, p. 185-189, 2011. pdf
• On the arithmetic nature of hypertranscendental functions at complex points. Expositiones Mathematicae, v. 29, p. 361-370, 2011. pdf
• On Integer Numbers with Locally Smallest Order of Appearance in the Fibonacci Sequence. International Journal of Mathematics and Mathematical Sciences, v. 2011, p. 1-4, 2011. pdf
• (with A. Togbé) On terms of linear recurrence sequences with only one distinct block of digits. Colloquium Mathematicum, v. 124, p. 145-155, 2011. pdf
• The Fibonacci version of a variant of the Brocard-Ramanujan Diophantine equation. Far East Journal of Mathematical Sciences: FJMS, v. 56, p. 219-224, 2011. pdf

#### 2010

• (with F. Luca) Perfect powers in the summatory function of power tower. Journal de théorie des nombres de Bordeaux, v. 22, p. 703-718, 2010.
• (with J. Huang and M. Mereb) Algebraic Values of Transcendental Functions at Algebraic Points. Bulletin of the Australian Mathematical Society, p. 1-6, 2010. pdf
• (with J. Sondow) Algebraic, irrational, and transcendental solutions of some exponential equations. Annales Mathematicae et Informaticae, v. 37, p. 151-164, 2010. link
• Algebraic numbers of the form $$P(T)^{Q(T)}$$ with $$T$$ transcendental. Elemente der Mathematik, p. 78-80, 2010. pdf
• (with A. Togbé) Perfect powers among Fibonomial coefficients. Comptes Rendus. Mathématique, v. 348, p. 717-720, 2010. pdf
• (with C. Jensen) Some Field Theoretic Properties and an Application Concerning Transcendental Numbers. Journal of Algebra and its Applications, v. 09, p. 493-500, 2010. pdf
• (with J. Sondow) Schanuel conjecture and the algebraic powers $$z^w$$ and $$w^z$$ with $$z$$ and $$w$$ transcendental. East-West Journal Mathematics, v. 12, p. 75-84, 2010. pdf
• (with A. Togbé) On the sum of powers of two consecutive Fibonacci numbers. Proceedings of the Japan Academy. Series A Mathematical Sciences, v. 86, p. 174-176, 2010. link
• (with G. G. Bastos) On the Diophantine equation $$3^{2n}-2\cdot 3^m+1=k^2$$. Journal of Algebra, Number Theory: Advances and Applications, v. 4, p. 91-104, 2010. pdf

#### 2009

• A Geometric Proof to Cantor's Theorem and an Irrationality Measure for Some Cantor's Series. Annales Mathematicae et Informaticae, v. 36, p. 117-121, 2009. link
• (with F. Luca and P. Stanica) On the spacings between $$C$$-nomial coefficients. Journal of Number Theory (Print), v. 130, p. 82-100, 2009. pdf
• (with C. Cheng, B. Dietel, M. Herblot, J. Huang, H. Krieger, J. Mason, M. Mereb and S. Wilson) Some Consequences of Schanuel's Conjecture. Journal of Number Theory, v. 129, p. 1464-1467, 2009. pdf