Number theory · Modular arithmetic · Power towers · Multiplicative order
Determine whether the number
\[ 10^{5^{10^{5^{10}}}} + 5^{10^{5^{10^{5}}}} \]
is divisible by \(11\).
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Serbian Municipal Competition 2008, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source