A = 25.3.( 4^1999 + 4^1998 + ... + 4^2 + 4 +1 ) + 25
= 25.[4.( 4^1999 + 4^1998 + ... + 4^2 + 4 +1 ) - ( 4^1999 + 4^1998 + ... + 4^2 + 4 +1 )] + 25
= 25.[4.( 4^2000 + 4^1999 + 4^1998 ... + 4^2 + 4 ) - ( 4^1999 + 4^1998 + ... + 4^2 + 4 +1 )] + 25
= 25.( 4^2000 -1 ) + 25
= 25.( 4^2000 -1 + 1 )
= 25. 4^2000
= 25.4.4^2000
= 100.4^2000
=> A chia hết cho 100