| Abstract: | We propose an efficient search algorithm to solve the equation  for a fixed value of  . By parametrizing  , this algorithm obtains  and  (if they exist) by solving a quadratic equation derived from divisors of  . Thanks to the use of several efficient number-theoretic sieves, the new algorithm is much faster on average than previous straightforward algorithms. We performed a computer search for six values of  below 1000 for which no solution had previously been found. We found three new integer solutions for  and 931 in the range of  . |
