Abstract: This article presents a solution to exponentiation remainder problems. When the base and modulus are coprime, Euler's theorem can be directly applied. If not, a transformation is needed before applying it. The article demonstrates this method through multiple examples. For common exponentiation last-digit problems in exams, just retain the last digit of the base and take the exponent modulo 4 for quick solutions when the modulus is 10. Overall, this article offers an effective and systematic approach to solving exponentiation remainder problems, with both theoretical and practical value.

Key words: divisibility, power, remainder