On some inequalities connected with Fermat's equation.
On Sophie Germain type criteria for Fermat's Last Theorem
On square values of quadratics
On the Catalan equation over algebraic number fields.
On the congruence , where q is a prime and f is a polynomial
On the congruence f(x) + g(y) + c ≡ 0 (mod xy) (completion of Mordell's proof)
Assertions on the congruence f(x) + g(y) + c ≡ 0 (mod xy) made without proof by Mordell in his paper in Acta Math. 88 (1952) are either proved or disproved.
On the Diophantine Equation 2x3 + 1 = py2.
On the Diophantine equation .
On the diophantine equation
On the Diophantine equation ax...+bx...y+cy...=d and pure powers in recurrence sequences.
On the Diophantine Equation Cx2 + D = 2yn.
On the diophantine equation f (x, y) = 0.
On the diophantine equation f(x)f(y) = f(z)²
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.
On the Diophantine equation F(x)=G(y)
On the Diophantine equation f(y) - x = 0
On the Diophantine equation
On the diophantine equation
On the diophantine equation
Consider the equation in the title in unknown integers with , , , , and . Under the above conditions we give all solutions of the title equation (see Theorem 1).
On the diophantine equation
On the Diophantine equation