Write the exact powers of 2 and 3 in sorted order as 1, 2, 3, 4, 8, 9, 16, 27, 32, ... (OEIS A006899), and let be the th term in the sequence. Then tends to infinity nearly as rapidly as .

# Pillai's Theorem

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## References

Hardy, G. H.*Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed.*New York: Chelsea, 1999.Pillai.

*J. Indian Math. Soc.*

**19**, 1-11, 1931.Sloane, N. J. A. Sequence A006899/M0588 in "The On-Line Encyclopedia of Integer Sequences."

## Referenced on Wolfram|Alpha

Pillai's Theorem## Cite this as:

Weisstein, Eric W. "Pillai's Theorem."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/PillaisTheorem.html