Number theory · Digit problems · Divisibility by 9 · Parity · Bounding · Exhaustive check
Problem 2, 2025
← Prev · 1 / 37 · Next →Find all three-digit numbers \(\overline{abc}\) that are divisible by \(9\) and satisfy
\[ \overline{abc} = a^6 + b^2 + c^3, \]
where \(a\), \(b\), \(c\) denote the digits of the number.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), odbirno (qualifying) round 2025, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source