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Part of 1992 ITAMO

Problems(1)

n distinct divisors d_1,d_2, ...,d_n of n! with n! = d_1 +d_2 +···+d_n

Source: 1992 ITAMO p3

1/31/2020
Prove that for each n≥3n \ge 3 there exist nn distinct positive divisors d1,d2,...,dnd_1,d_2, ...,d_n of n!n! such that n!=d1+d2+...+dnn! = d_1 +d_2 +...+d_n.
Divisorsfactorialsum of divisorsnumber theory