Erdős Problem #242 [status

falsifiable; formalized: yes]. For every $n>2$ there exist distinct integers $1\leq x<y<z$ such that$$\frac{4}{n} = \frac{1}{x}+\frac{1}{y}+\frac{1}{z}.$$ Current best: Schinzel conjectured the generalisation that, for any fixed $a$, if $n$ is sufficiently large in terms of $a$ then there exist distinct integers $1\leq x<y<z$ such that$$\frac{a}{n} = \frac{1}{x}+\frac{1}{y}+\frac{1}{z}.$$This problem has been formalised in Lean as part of the Google DeepMind Formal Conjectures project. Prize: no. OEIS: A073101, A075245, A075246, A075247, A075248, A287116. Tags: number theory, unit fractions.

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