Jebelean-Weber´s algorithm without spurious factors

Tudor Jebelean and Ken Weber introduced in [10, 4] an algorithm for finding a (a, b)-pairs satisfying au + bv equiv 0 (mod k), with 0 < |a|, |b|< radic(k). It is based on Soren- son\´s "k-ary reduction" algorithm ([9]). One of the major drawbacks is that this algorithm do not preserves the GCD\´s. We present a modified version which avoids this problem.