Number theory · Digit sums · Repunits · Congruences mod 9 · Borrowing
Find the smallest natural number \(n\) for which there exist natural numbers \(a\) and \(b\) whose digit sums are \(28\) and \(21\) respectively, and
\[ a + b = \underbrace{11\ldots1}_{n}. \]
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Serbian Regional Competition (Okruzno takmicenje) 2021, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source