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Problem 6 - Entrance Test

What is the remainder when 3^203 is divided by 5?

Correct: C

We look for a pattern in the remainders of powers of 3 when divided by 5. 3^1 % 5 = 3. 3^2 % 5 = 9 % 5 = 4. 3^3 % 5 = 27 % 5 = 2. 3^4 % 5 = 81 % 5 = 1. 3^5 % 5 = 243 % 5 = 3. The remainders repeat every 4 powers: 3, 4, 2, 1. 203 divided by 4 is 50 with a remainder of 3. Therefore, 3^203 % 5 is the same as 3^3 % 5, which is 2.