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Part of 1989 Mexico National Olympiad

Problems(1)

1989-digit natural number such that product of its digits = their sum and ...

Source: Mexican Mathematical Olympiad 1989 OMM P3

7/27/2018
Prove that there is no 19891989-digit natural number at least three of whose digits are equal to 55 and such that the product of its digits equals their sum.
number theorysum of digits