Waste less time on Facebook — follow Brilliant.
×

Near Catalan's Equation

From Catalan's theorem, we know that \(3^2 - 2^3 = 1\) is the only solution to the following equation, for some integers \(a,b \geq 1\) and \(x,y \geq 2\):

\[a^x - b^y = 1\]

Now is there any theorem confirming for \(3^3 - 5^2 = 2\) as the the only solution to the equation:

\[a^x - b^y = 2\]

as well?

Any reference to any paper would be appreciated. Thank you.

Note by Worranat Pakornrat
1 month, 3 weeks ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

no there isn't it is still a conjecture that there are finite many solutions to the equation \[a^x - b^y = n\] where \[n>1, n \in \mathbb{N} \]

Kaito Einstein - 1 month, 3 weeks ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...