A remark on a Diophantine equation of S. S. Pillai
摘要
S. S. Pillai proved that for a fixed positive integer a, the exponential Diophantine equation xy − yx = a, min(x,y) > 1, has only finitely many solutions in integers x and y. We prove that when a is of the form 2z2, the above equation has no solution in integers x and y with gcd(x,y) = 1.