# Blog Archives

## IMO 1983 – Problem 3

Let and be positive integers and let be a set of points in the plane such that

no three points of are collinear, and

for any point of , there are at least points of equidistant from

Prove that

Try the question …

Solution will be updated soon

## IMO 2007 Short list problem

Find all functions such that

for all x,y

**Solution :**

For any positive real numbers , we have that

and by Cauchy in positive reals, then for all

Now it’s easy to see that , then for all positive real numbers

## Problem Of the Day-2

Here is Yesterday Problem

Yesterday Winner was Akash Agarwal

You must be knowing that If you win the Problem of the day for 4 times in a week – then I will send you a Really interesting book on any topic you want 🙂

Today’s Problem :

Find all possible values of x satisfying :

[x]/[x-2] – [x-2]/[x] = (8{x} + 12)/([x-2][x])

(.) = Normal bracket

{.} = Fractional part function

[.] = GIF/Floor function