`a)`
Ta có :
`A = 2012 . 2014 = (2013 - 1)(2013 + 1) = 2013^2 - 1`
`B = 2013 . 2013 = 2013^2`
Ta thấy :
`2013^2 - 1 < 2013^2`
`=> 2012 . 2014 < 2013 .2013`
`=> A < B`
`b)`
Ta có :
`C = 24 . (5^2 + 1)(5^4 + 1)(5^8 +1)(5^16 + 1)`
`= (5^2 - 1)(5^2 + 1)(5^4 + 1)(5^8 + 1)(5^16 + 1)`
` = (5^4 - 1)(5^4 + 1)(5^8 + 1)(5^16 + 1)`
`= (5^8 -1)(5^8 + 1)(5^16 + 1)`
`= (5^16-1)(5^16+ 1)`
` = 5^32 -1`
`D = 25^16 = (5^2)^16 = 5^32`
Ta thấy :
`5^32 - 1 < 5^32`
`=> C < D`
