This note is to show how can be used very effectively to solve olympaid problems .
To explain its significance a example of question of
QUESTION : Find all integers such that roots of are integers.
Proof : let are integral roots of
Since are integers and therefore atleast one of them is even or but doesn’t give integral roots but therefore at a time 2 or 3 of can’t be even .
Therefore only one of them is even .
Let is even .
, this implies for be an integer is also an integer . Now put (because at the term diappeas in ) in this gives . Now since is even therefore where is the essential case as makes .
So is a root of . after putting values of in we get which matches our condition that .