Paul Erdős died in 1996, but his most recent paper is from 2015, nearly 20 years later! There's a writeup at simonsfoundation.org/2015/12/1; the paper itself is math.ucsd.edu/~ronspubs/pre_tr

It's about Egyptian fractions – representations of rationals as sums of distinct unit fractions – and is motivated by the conjecture that it's always possible for all denominators to be semiprime. That's still open, but they prove that every integer has a representation with all denominators products of three primes.

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