Displaying similar documents to “Lucas balancing numbers”

Counting Keith numbers.

Klazar, Martin, Luca, Florian (2007)

Journal of Integer Sequences [electronic only]

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On the Euler function of repdigits

Florian Luca (2008)

Czechoslovak Mathematical Journal

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For a positive integer n we write φ ( n ) for the Euler function of n . In this note, we show that if b > 1 is a fixed positive integer, then the equation φ x b n - 1 b - 1 = y b m - 1 b - 1 , where x , y { 1 , ... , b - 1 } , has only finitely many positive integer solutions ( x , y , m , n ) .

On the powerful part of n 2 + 1

Jan-Christoph Puchta (2003)

Archivum Mathematicum

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We show that n 2 + 1 is powerfull for O ( x 2 / 5 + ϵ ) integers n x at most, thus answering a question of P. Ribenboim.