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## Problem – Gauss Trick (ISI Entrance)

Let’s learn Gauss Trick for ISI Entrance.

If k is an odd positive integer, prove that for any integer $ \mathbf{ n \ge 1 , 1^k + 2^k + \cdots + n^k } $ is divisible by $ \mathbf{ \frac {n(n+1)}{2} } $

**Key Concepts**

**Gauss Trick**

**Factoring Binomial**

## Source

But try the problem first…

From I.S.I. Entrance and erstwhile Soviet Olympiad.

Source

Suggested Reading

Test of Mathematics at 10+2 Level by East West Press, Subjective Problem 31

Challenges and Thrills of Pre College Mathematics

## Try the first hint

## Other useful links:-

- https://www.cheenta.com/complex-number-isi-entrance-b-stat-hons-2003-problem-5/
- https://www.youtube.com/watch?v=P4ZYA4XCQoM&list=PLTDTcDkWcXuxeaAMvWpx4vGIul38dKOQp&index=4