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Part of 2015 Portugal MO

Problems(1)

firm 3-digit numbers - Portugal OPM 2015 p1

Source:

5/15/2024
A number of three digits is said to be firm when it is equal to the product of its unit digit by a number formed by the remaining digits. For example, 153153 is firm because 153=3×51153 = 3 \times 51. How many firm numbers are there?
number theory