Brocard's problem
Template:Non-polynomial diophantine
Statement
Brocard's problem asks for all pairs of positive integers such that:
.
The only known solutions are . The s that occur as part of such solution pairs are termed Brown numbers. It is conjectured that there are no other solutions.
Related facts
- abc conjecture implies that the number of solutions to this equation is finite. Further information: anc conjecture implies finitely many Brown numbers