Power n divisible by n powers

Number Theory Level 4

If \(S\) is the sum of all possible positive integers \(n\) such that \(\dfrac {10^n} {n^3+n^2+n+1} \) is an integer, what is the remainder when \(S\) is divided by 10?

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Power n divisible by n powers

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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.