On the diophantine equation 27y2 + 4x3 = M.
On the Diophantine Equation 2x3 + 1 = py2.
On the Diophantine equation .
On the diophantine equation
On the Diophantine Equation Ax4 -By2 = C (C = 1, 4).
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
On the Diophantine equation .
On the diophantine equation D₁x⁴ -D₂y² = 1
On the diophantine equation
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 for third order linear recurring sequences.
On the Diophantine equation
Let denote the term of the Fibonacci sequence. In this paper, we investigate the Diophantine equation in the positive integers and , where and are given positive integers. A complete solution is given if the exponents are included in the set . Based on the specific cases we could solve, and a computer search with we conjecture that beside the trivial solutions only , , and satisfy the title equation.
On the Diophantine equation
On the Diophantine equation
On the diophantine equation
P. 294, line 14: For “Satz 8” read “Satz 7”, and for “equation (10)” read “equation (13)”.