MathDB

2

Part of 2014 India National Olympiad

Problems(1)

Prove that expression is always even.

Source: INMO 2014- Problem 2

2/2/2014
Let nn be a natural number. Prove that, ⌊n1⌋+⌊n2⌋+⋯+⌊nn⌋+⌊n⌋ \left\lfloor \frac{n}{1} \right\rfloor+ \left\lfloor \frac{n}{2} \right\rfloor + \cdots + \left\lfloor \frac{n}{n} \right\rfloor + \left\lfloor \sqrt{n} \right\rfloor is even.
floor functionnumber theory unsolvednumber theory