Catalan’s Conjecture: Another old Diophantine problem solved
Catalan’s Conjecture: Another old Diophantine problem solved
Catalan’s Conjecture predicts that 8 and 9 are the only consecutive perfect powers among positive integers. The conjecture, which dates back to 1844, was recently proven by the Swiss mathematician Preda Mihăilescu. A deep theorem about cyclotomic fields plays a crucial role in his proof. Like Fermat’s problem, this problem …