For every 
,
there exist only finite many pairs of powers 
with 
and 
natural numbers and 
.
Pillai's Conjecture
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References
Ribenboim, P. "Catalan's Conjecture." Amer. Math. Monthly 103, 529-538, 1996.Referenced on Wolfram|Alpha
Pillai's ConjectureCite this as:
Weisstein, Eric W. "Pillai's Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PillaisConjecture.html