Problem #242: For every $n>2$ there exist distinct integers $1\leq x

For every $n>2$ there exist distinct integers $1\leq x

SOLVED

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Progress

The Erdős-Straus conjecture. The existence of a representation of $4/n$ as the sum of at most four distinct unit fractions follows trivially from a greedy algorithm.

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.