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Pell and Pell-Lucas numbers of the form $- 2^{a} - 3^{b} + 5^{c}$

Yunyun Qu, Jiwen Zeng (2020)

Czechoslovak Mathematical Journal

In this paper, we find all Pell and Pell-Lucas numbers written in the form $- 2^{a} - 3^{b} + 5^{c}$ , in nonnegative integers $a$ , $b$ , $c$ , with $0 \leq max {a, b} \leq c$ .

Perfect powers in arithmetical progression (II)

T. N. Shorey, R. Tijdeman (1992)

Compositio Mathematica

Perfect powers in products of integers from a block of consecutive integers (II)

T. N. Shorey, Yu. V. Nesterenko (1996)

Acta Arithmetica

Perfect powers in products of terms in an arithmetical progression III

T. N. Shorey, R. Tijdeman (1992)

Acta Arithmetica

Perfect powers in products of terms in an arithmetical progression (II)

T. N. Shorey, R. Tijdeman (1992)

Compositio Mathematica

Perfect powers in products of terms in an arithmetical progression

T. N. Shorey, R. Tijdeman (1990)

Compositio Mathematica

Perfect powers in q-binomial coefficients

Florian Luca (2012)

Acta Arithmetica

Perfect powers in the summatory function of the power tower

Florian Luca, Diego Marques (2010)

Journal de Théorie des Nombres de Bordeaux

Let ${(a_{n})}_{n \geq 1}$ be the sequence given by $a_{1} = 1$ and $a_{n} = n^{a_{n - 1}}$ for $n \geq 2$ . In this paper, we show that the only solution of the equation $a_{1} + \dots + a_{n} = m^{l}$ is in positive integers $l > 1, m$ and $n$ is $m = n = 1$ .

Perfect powers with all equal digits but one.

Kihel, Omar, Luca, Florian (2005)

Journal of Integer Sequences [electronic only]

Primitive divisors of certain elliptic divisibility sequences

Paul Voutier, Minoru Yabuta (2012)

Acta Arithmetica

Products of integers in short intervals

P. Erdös, J. Turk (1984)

Acta Arithmetica

Pure powers and power classes in recurrence sequences

Péter Kiss (1994)

Mathematica Slovaca

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