# 100 followers problem!

**Number Theory**Level 3

The diagonal of the square with side 100 cm can be expressed as \(a\times\sqrt b cm\) and b is Square Free.

Then X=ab

Let Y be the number of trailing zeroes in 100!

Let the roots of the quadratic equation \({x}^{2} + 100 x + 819\) be p and q

Then \({p}^{2} + {q}^{2} = Z\)

Let A be the number of trailing zeroes in (X+Y+Z)!

Find \(X+Y+Z+A \)