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# Gauss Trick in ISI Entrance

Gauss trick can be used to solve tricky algebra problems. Learn it in this self-learning module for ISI Entrance and math olympiad

## 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

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

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

Challenges and Thrills of Pre College Mathematics

## By Dr. Ashani Dasgupta

Ph.D. in Mathematics, University of Wisconsin, Milwaukee, United States.

Research Interest: Geometric Group Theory, Relatively Hyperbolic Groups.

Founder, Cheenta

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