`a/2003 = b/2004 = c/2005`
` = `$\dfrac{a - b}{2003 - 2004}$` = `$\dfrac{b - c}{2004 - 2005}$` = `$\dfrac{c - a}{2005 - 2003}$
`(=)` $\dfrac{a - b}{-1}$` = `$\dfrac{b - c}{-1}$` = `$\dfrac{c - a}{2}$
`=> `$\dfrac{(c - a)^{2}}{2^{2}}$` = `$\dfrac{a - b}{-1}$` . `$\dfrac{b - c}{-1}$
`=> `$\dfrac{(c - a)^{2}}{4}$` = `$\dfrac{(a - b)(b - c)}{(-1)(-1)}$
`=> (c - a)^2 = 4(a - b)(b - c).`