# Brocard's problem

From Number

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`