If $16^3^{31} - 33$ is divided by 10, then the remainder obtained is
Step-by-Step Solution
Key Concept: Divisibility of differences of powers can be analyzed using algebraic factorization and modular arithmetic.
We use the factorization $x^n - y^n = (x-y)(x^{n-1} + x^{n-2}y + \ldots + xy^{n-2} + y^{n-1})$. For $5^3 - 3^3 = 53^3$, we rewrite as $(50-30) + (3^3 - 3^3) = 3^3(50-1) - 27 = 3^3(10^2 - 1) - 27 = 27(108-1) - 27 = 270 - 54 = 270 - 60 + 6 = 10y + 6$. Hence the remainder is $6$.
Correct Answer: 6