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Question

What is the remainder when the sum of the first 102 counting numbers is divided by 5250? (The first counting number is 1.)

Accepted Answer

For all n, 1 + 2 + + n = n(n + 1)/2, so 1 + 2 + + 102 = 102 103/2 = 5253. The remainder when 5253 is divided by 5250 is 3.