Last Two Digits of a Term

★ 6/10number theory Recursion Modular Arithmetic sequences Induction

Problem

A sequence $\{a_n\}$ satisfies $a_1 = 1$ , $a_2 = 2$ , and for $k \in \mathbb{N}^+$ ,

a_{2k+1} = \frac{a_{2k}^2}{a_{2k-1}}, \qquad a_{2k+2} = 2a_{2k+1} - a_{2k}.

Find the last two digits of $a_{2022}$ .

Answer

Solution

Difficulty	6/10
Topics	number theory, Recursion, Modular Arithmetic, sequences, Induction

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