Displaying similar documents to “Some observations on the Diophantine equation f(x)f(y) = f(z)²”

Parametric Solutions of the Diophantine Equation A² + nB⁴ = C³

Susil Kumar Jena (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

The Diophantine equation A² + nB⁴ = C³ has infinitely many integral solutions A, B, C for any fixed integer n. The case n = 0 is trivial. By using a new polynomial identity we generate these solutions, and then give conditions when the solutions are pairwise co-prime.

On the diophantine equation f(x)f(y) = f(z)²

Maciej Ulas (2007)

Colloquium Mathematicae

Similarity:

Let f ∈ ℚ [X] and deg f ≤ 3. We prove that if deg f = 2, then the diophantine equation f(x)f(y) = f(z)² has infinitely many nontrivial solutions in ℚ (t). In the case when deg f = 3 and f(X) = X(X²+aX+b) we show that for all but finitely many a,b ∈ ℤ satisfying ab ≠ 0 and additionally, if p|a, then p²∤b, the equation f(x)f(y) = f(z)² has infinitely many nontrivial solutions in rationals.