Number theory · Digit sums · Perfect squares · Decimal representation · Congruences mod 9 · Repunits · Explicit constructions
Does there exist a natural number which is a perfect square and whose sum of digits equals \(2008^{2009}\)?
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Serbian National Competition (Drzavno takmicenje) 2009, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source