What is the remainder when is divided by 5?

4. Using modulo 5 properties: . Next, . Finally, . The sum is , so the remainder is 4.

What is the remainder when 111^{222}+222^{333}+333^{444} is divided by 5?

A. 1
B. 2
C. 3
D. 4 ✓

Correct Answer: D. 4

Explanation

Using modulo 5 properties: 111 \equiv 1 \implies 1^{222} = 1. Next, 222 \equiv 2 \implies 2^{333} = 2 \times (2^4)^{83} \equiv 2 \times 1 = 2. Finally, 333 \equiv 3 \implies 3^{444} = (3^4)^{111} \equiv 1. The sum is 1 + 2 + 1 = 4, so the remainder is 4.

What is the remainder when 111^{222}+222^{333}+333^{444} is divided by 5?

Explanation

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