On the difference between perfect powers
On the difference of cubes (mod p)
On the Diophantine equation 1 + x + y = z, with xyz = 2r3s7t.
On the Diophantine equation
Let be an odd prime. By using the elementary methods we prove that: (1) if , the Diophantine equation has no positive integer solution except when or is of the form , where is an odd positive integer. (2) if , , then the Diophantine equation has no positive integer solution.
On the diophantine equation 27 y2 + 4 x3 = D.
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