Are there infinitely many solutions to frac1p_1+…+frac1p_k=1-frac1m, where m≥ 2 is an integer and p_1<…<p_k are distinct primes?

Erdős Problem #313 — Are there infinitely many solutions to $\frac{1}{p_1}+\cdots+\frac{1}{p_k}=1-\frac{1}{m},$ where $m\geq 2$ is an integer and $p_1<\cdots<p_k$ are distinct primes?

About 46 years old · traced to 1980

Are there infinitely many solutions to $\frac{1}{p_1}+\cdots+\frac{1}{p_k}=1-\frac{1}{m},$ where $m\geq 2$ is an integer and $p_1<\cdots<p_k$ are distinct primes?

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.

number-theory unit-fractions

InErdős Problems

Posted 1 month ago · edited 3 weeks ago

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