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(381) 3

Part of 1993 Tournament Of Towns

Problems(1)

TOT 381 1993 Autumn O J3 A-> A+d NT

Source:

6/12/2024
A natural number AA is given. One may add to it one of its divisors dd (1<d<A1 < d < A). One may then repeat this operation with the new number A+dA + d and so on. Prove that starting from A=4A = 4 one can get any composite number by these operations.
(M Vyalyi)
number theoryDivisors