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MathNet 1984 — Part 01 Question 7

Math Olympiad Vault · MathNet 1984 — Part 01

Question 7

An integer is digitally divisible if

(a) none of its digits is zero;

(b) it is divisible by the sum of its digits (e.g., $322$ is digitally divisible).
Show that there are infinitely many digitally divisible integers.