`text(Ta có :)`
`a^2000 + b^2000 = a^2001 + b^2001 = a^2002 + b^2002`
`⇒ a^2002 + b^2002 = a(a^2001 + b^2001) + b(a^2001 + b^2001) - b(a^2001 + b^2001)`
` = (a + b)(a^2001 + b^2001) - ba(a^2000 + b^2000)`
`Do a^2000 + b^2000 = a^2001 + b^2001 = a^2002 + b^2002`
`⇒ (a + b)(a^2001 + b^2001) - ba(a^2000 + b^2000)`
`= (a + b)(a^2001 + b^2001) - ba(a^2001 + b^2001) = a^2002 + b^2002`
`⇔ (a^2001 + b^2001)(a + b - ab) = a^2002 + b^2002`
`⇔ a + b - ab = 1`
⇔
`text(Ta có :)`
`(a + b) - ab = 1`
`⇔ a + b - ab = 1`
`⇔ ab - a - b + 1 = 0`
`⇔ a(b - 1) - (b - 1) = 0`
`⇔ (a - 1)(b - 1) = 0`
`⇒` \(\left[ \begin{array}{l}a = 1\\b = 1\end{array} \right.\)
`text(Ta có :)`
`b^2000 = b^2001`
`⇔ b^2001 - b^2000 = 0`
`⇔ b^2000(b - 1) = 0`
`⇔` \(\left[ \begin{array}{l}b = 0\\b = 1\end{array} \right.\)
