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On some generalizations of the diophantine equation $s(1^{k} + 2^{k} + ⋯ + x^{k}) + r = dy^{n}$

100%

Rakaczki C.

Acta Arithmetica

2012

tom 151

nr 2

201-216

On the diophantine equation x(x-1)...(x-(m-1)) = λy(y-1 )...(y-(n-1)) + l

100%

Rakaczki C.

Acta Arithmetica

2003

tom 110

nr 4

339-360

Diophantine equations with Euler polynomials

63%

Kreso D., Rakaczki C.

Acta Arithmetica

2013

tom 161

nr 3

267-281

We determine decomposition properties of Euler polynomials and using a strong result relating polynomial decomposition and diophantine equations in two separated variables, we characterize those g(x) ∈ ℚ [x] for which the diophantine equation $-1^k + 2^k - ⋯ + (-1)^{x} x^k = g(y)$ with k ≥ 7 may have infinitely many integer solutions. Apart from the exceptional cases we list explicitly, the equation has only finitely many integer solutions.

Ograniczanie wyników

3 Acta Arithmetica

3 Rakaczki C.

1 Kreso D.

1 2013

1 2012

1 2003

Wyniki wyszukiwania

On some generalizations of the diophantine equation $s(1^{k} + 2^{k} + ⋯ + x^{k}) + r = dy^{n}$

On the diophantine equation x(x-1)...(x-(m-1)) = λy(y-1 )...(y-(n-1)) + l

Diophantine equations with Euler polynomials