1977 Canadian MO Problems/Problem 1
Problem
If prove that the equation
has no solutions in positive integers
and
Solution
Directly plugging and
into the function,
We now have a quadratic in
Applying the quadratic formula,
![$\displaystyle a=\frac{-1\pm \sqrt{b^2+b+1}}{2}.$](http://latex.artofproblemsolving.com/6/c/2/6c20f5c70bcc36ce41ad815a7404de3422176172.png)
Because, the quantity
cannot be a perfect square when
is an integer. Hence, when
is a positive integer,
cannot be.