### Mean square of the remainder term in the Dirichlet divisor problem II

Kai-Man Tsang (1995)

Acta Arithmetica

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Kai-Man Tsang (1995)

Acta Arithmetica

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Liu, Huili (2004)

Beiträge zur Algebra und Geometrie

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D. R. Heath-Brown (1995)

Acta Arithmetica

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Michael R. Avidon (1996)

Acta Arithmetica

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Peter Söhne (1993)

Acta Arithmetica

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E. Carletti, G. Monti Bragadin (1995)

Acta Arithmetica

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Jürgen G. Hinz (1996)

Acta Arithmetica

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Pavel M. Bleher, Freeman J. Dyson (1994)

Acta Arithmetica

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Maohua Le (1997)

Acta Arithmetica

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1. Introduction. Let ℤ, ℕ, ℚ be the sets of integers, positive integers and rational numbers respectively. In [7], Ribenboim proved that the equation (1) $({x}^{m}+1)({x}^{n}+1)=y\xb2$, x,y,m,n ∈ ℕ, x > 1, n > m ≥ 1, has no solution (x,y,m,n) with 2|x and (1) has only finitely many solutions (x,y,m,n) with 2∤x. Moreover, all solutions of (1) with 2∤x satisfy max(x,m,n) < C, where C is an effectively computable constant. In this paper we completely determine all solutions of (1) as follows. Theorem....