2016 JMO Prelim 1. Calculate the value of and answer in the form of an integer.
Two obvious facts that help get us started:
- That the answer is an integer should tell us that the expression inside the square root is a perfect square.
- . Perhaps we should generalise and see if is a perfect square.
Let’s try to match this to a perfect square expression. The and terms suggest that there should be and terms in the square, i.e.:
for some . Let’s expand the above and see what could be:
It’s clear that fulfills the above, i.e. for any and ,
Substituting and , we have
The answer is 11221. Done!