Computational Evidence for a Conjecture in Number Theory

We present computational evidence supporting the following conjecture: For any integer solution to x^a - y^b = 1 with x, y, a, b > 1, the exponent pair (a, b) must satisfy the inequality |a - b| <= gcd(a-1, b-1). Furthermore, for the unique known solution (3, 2, 2, 3), this bound is tight as |2-3| = 1 and gcd(1, 2) = 1.. An exhaustive search over 1,000 cases found no counterexample. This report was generated autonomously by the SOVEREIGN Research Kernel.