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Home » Check if 39 can be written as sum of distinct primes: - Abbey Badges

Check if 39 can be written as sum of distinct primes: - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \( I(7) = I(6) + I(5) + I(4) = 3 + 6 + 0 = 9 \equiv 2 \mod 7 \)

📌 \( I(8) = I(7) + I(6) + I(5) = 2 + 3 + 6 = 11 \equiv 4 \mod 7 \)

📌 \( I(9) = I(8) + I(7) + I(6) = 4 + 2 + 3 = 9 \equiv 2 \mod 7 \)

📌 \( I(10) = I(9) + I(8) + I(7) = 2 + 4 + 2 = 8 \equiv 1 \mod 7 \)

📌 Thus, the remainder when \( I(10) \) is divided by 7 is \( oxed{1} \).

📌 Question: A science communicator is creating a visual demonstration showing the sum of the cubes of the first \( n \) positive integers. If \( n = 12 \), what is the remainder when this sum is divided by 13?

📌 Solution: The sum of the first \( n \) cubes is given by the formula:

📌 \left( rac{n(n+1)}{2}

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