Is it true that in any finite colouring of the integers there exists a monochromatic solution
to $\frac 1 a = \frac 1 b + \frac 1 c$ with distinct $a, b, c$?
This is true, as proved by Brown and RΓΆdl [BrRo91].
[BrRo91] Brown, Tom C. and RΓΆdl, Voijtech,
_Monochromatic solutions to equations with unit fractions_.
Bull. Austral. Math. Soc. (1991), 387-392.
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theorem erdos_303 :
answer(True) β
-- For any finite colouring of the integers
β (π : β€ β β€), (Set.range π).Finite β
-- There exists integers `a, b, c`
β (a b c : β€),
-- that are non-zero and distinct.
[a, b, c, 0].Nodup β§
-- `a, b, c` satisfy the equation
(1/a : β) = 1/b + 1/c β§
-- `a, b, c` have the same color
(π '' {a, b, c}).Subsingleton
