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Erdős Problem #406 — Is it true that there are only finitely many powers of 22 which have only the digits 00 and 11 when written in base 33?

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Is it true that there are only finitely many powers of 22 which have only the digits 00 and 11 when written in base 33?

References

Primary source

ULAM AI, UnsolvedMath dataset, Erdős Problems set, revision b9437975f3c873f635a13c48f8b022f5ba80898a; CC BY 4.0.

Additional references

UnsolvedMath, Erdős Problems set, ULAM AI, licensed CC BY 4.0.

base-representationsnumber-theory
InErdős Problems
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