Number theory · Decimal representation · Products of consecutive integers · Bounding · Base representation
Determine all nonnegative integers \(n\) and all digits \(a\), \(b\), \(c\) for which the number
\[ M = \overline{1\,\underbrace{0 \dots 0}_{n}\,a\,\underbrace{0 \dots 0}_{n}\,b\,\underbrace{0 \dots 0}_{n}\,c} \]
- that is, the number whose decimal notation consists of the digit \(1\), then \(n\) zeros, then the digit \(a\), then \(n\) zeros, then the digit \(b\), then \(n\) zeros, and finally the digit \(c\) - is a product of three consecutive natural numbers.
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Serbian National Competition (Drzavno takmicenje) 2020, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source