Number theory · Exponential diophantine equations · 2 adic valuation · Difference of powers · Congruences mod 8
Solve the equation
\[ 20^x + 2^y = 2022^z \]
in the set of natural numbers.
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Serbian Regional Competition (Okruzno takmicenje) 2022, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source