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} } $
Gauss Trick
Factoring Binomial
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
