Question

What is the remainder when $(1^1+2^2+3^3+...+{100}^{100})$ is divided by 4?

• A. 1
• B. 2
• C. 3

Answer 1

There are 50 odd numbers and 50 even numbers. Every even number will be divisible by 4. Further, in odd numbers, half of them have 1 as the remainder and half of them have - 1 as the remainder. Then, the overall remainder is zero.