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3

Part of 1974 Czech and Slovak Olympiad III A

Problems(1)

Sum of permutated digits

Source: Czech and Slovak Olympiad 1974, National Round, Problem 3

7/19/2024
Let m≥10m\ge10 be any positive integer such that all its decimal digits are distinct. Denote f(m)f(m) sum of positive integers created by all non-identical permutations of digits of m,m, e.g. f(302)=320+023+032+230+203=808.f(302)=320+023+032+230+203=808. Determine all positive integers xx such that f(x)=138 012.f(x)=138\,012.
number theoryDigitssum of digitspermutationequationDiophantine equation