EUDML | On a Two-Dimensional Search Problem

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Displaying similar documents to “On a Two-Dimensional Search Problem”

Squares in $(1^{2} + m^{2}) \dots (n^{2} + m^{2})$ .

Ho, Pak Tung (2009)

Integers

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Large and small gaps between consecutive Niven numbers.

De Koninck, Jean-Marie, Doyon, Nicolas (2003)

Journal of Integer Sequences [electronic only]

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On the equation $a x^{n} - b y^{n} = c$

Jan-Hendrik Evertse (1982)

Compositio Mathematica

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On the congruence $N \equiv A (mod ϕ (N))$ .

Banks, William D., Güloğlu, Ahmet M., Nevans, C.Wesley (2008)

Integers

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Contributions to the theory of the distribution of prime numbers in arithmetical progressions III

Stanisław Knapowski (1962)

Acta Arithmetica

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Products of integers in short intervals

P. Erdös, J. Turk (1984)

Acta Arithmetica

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On two conjectures of Kátai

P. Elliott (1976)

Acta Arithmetica

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Neither $\prod_{k = 1}^{n} (4 k 2 + 1)$ nor $\prod_{k = 1}^{n} (2 k (k - 1) + 1)$ is a perfect square.

Fang, Jin-Hui (2009)

Integers

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On the largest prime factor of $n! + 2^{n} - 1$

Florian Luca, Igor E. Shparlinski (2005)

Journal de Théorie des Nombres de Bordeaux

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For an integer $n \geq 2$ we denote by $P (n)$ the largest prime factor of $n$ . We obtain several upper bounds on the number of solutions of congruences of the form $n! + 2^{n} - 1 \equiv 0 (mod q)$ and use these bounds to show that $\underset{n \to \infty}{lim sup} P (n! + 2^{n} - 1) / n \geq (2 π^{2} + 3) / 18 .$