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


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