Let k,l &gt;= 2 be fixed integers, and C be an effectively computable constant depending only on k and l. In this paper, we prove that all solutions of the equation (x + 1)(k) + (x + 2)(k) + ... + (lx)(k) = y(n) in integers x, y,n with x, y &gt;= 1, n &gt;= 2, k not equal 3 and l 1 (mod 2) satisfy max{x, y, n} &lt; C. The case when is even has already been completed by the second author (see [24]).

The Diophantine equation $(x+1)^k+(x+2)^k+\cdots+(\ell x)^k=y^n$ revisited

Abstract

Let k,l >= 2 be fixed integers, and C be an effectively computable constant depending only on k and l. In this paper, we prove that all solutions of the equation (x + 1)(k) + (x + 2)(k) + ... + (lx)(k) = y(n) in integers x, y,n with x, y >= 1, n >= 2, k not equal 3 and l 1 (mod 2) satisfy max{x, y, n} < C. The case when is even has already been completed by the second author (see [24]).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1534994
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