On the number of rational squares at fixed distance from a fifth power
  The main result of this note is that there are at most seven rational points (including the one at infinity) on the curve C_A with the affine equation y^2 = x^5 + A (where A is a tenth power free integer) when the Mordell-Weil rank of the Jacobian of C_A is one. This bound is attained for A = 18^2. 
Michael Stoll (International University Bremen)