Number theory · Exponential diophantine equations · Modular arithmetic · Factorization
Let \(\mathbb{N}_{0}=\mathbb{N}\cup\{0\}\). Determine all pairs \((a,b)\in\mathbb{N}_{0}\times\mathbb{N}_{0}\) for which
\[ 1+3^{a}+2025^{b}=2027^{b}. \]
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Regional Competition (Okruzno takmicenje) 2026, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source