Beal’s Conjecture states that if Ax + By = Cz for integers A,B,C > 0 and integers x,y,z > 2, then A, B, and C must share a common factor. Norvig and others have shown that the conjecture holds for A,B,C,x,y,z < 1000, but the truth of the general conjecture remains unresolved. Extending the search for a counterexample to significantly greater values of the conjecture's six integer parameters is a task ideally suited to the use of an SIMD parallel algorithm implemented on a GPGPU platform. This thesis project encompassed the design, coding, and testing of such an algorithm, implemented in the Brook+ language for execution on the AMD Firestream 9170 GPGPU.