Find the remainder when 5 + 52 + 53 + ……+ 555 is divided by 13.
Question
Find the remainder when 5 + 52 + 53 + ……+ 555 is divided by 13.
Solution
To solve this problem, we need to understand that the remainder of a sum is equal to the sum of the remainders.
Step 1: Find the remainder of each term when divided by 13.
5 mod 13 = 5 52 mod 13 = 0 53 mod 13 = 1 ... 555 mod 13 = 7
Step 2: Add up all the remainders.
5 + 0 + 1 + ... + 7 = 13
Step 3: Find the remainder of the sum when divided by 13.
13 mod 13 = 0
So, the remainder when 5 + 52 + 53 + ……+ 555 is divided by 13 is 0.
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