Number theory · Exponential diophantine equations · Modular arithmetic · Factorization
Problem 5, 2026
Let \(\mathbb{N}_{0}=\mathbb{N}\cup\{0\}\). Determine all pairs \((a,b)\in\mathbb{N}_{0}\times\mathbb{N}_{0}\) for which
\[ 1+3^{a}+2025^{b}=2027^{b}. \]
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Serbian Regional Competition (Okruzno takmicenje) 2026, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source