Question

Find the smallest positive whole number that when added to: 2001 x 2002 x 2004 x 2005 - 2003 x 2003 you get a square number

Answer 1

put
\[x=2003\] then you have
\[(x-2)(x-1)(x+1)(x+2)-x^2\]
\[(x^2-4)(x^2-1)-x^2\]
\[x^4-5x^2+4-x^2\]
\[x^4-6x^2+4\] to make this a perfect square add 5 to get
\[x^4-6x^2+9=(x^2-3)^2\]

Answer 2

so answer is 5