a, Ta có : `2^100` = `(2^4)^25` = `( . . .6 )^25` = ( . . . 6 )
`7^1991` = `7^1988` . `7^3` = `(7^4)^497` . `7^3` = `( . . . 1 )^497` . `7^3` = ( . . . 1 ) . ( . . . 3 ) = ( . . . 3 )
514 ≡ 5625 ( mod 10000 )
`=>` (514)2 ≡ 56252 ≡ 0625 ( mod 10000 )
`=>` (528)71 ≡ 0625 ( mod 10000 )
`=>` 51988 ≡ 0625 ( mod 10000 )
`=>` 54 ≡ 0625 ( mod 10000 )
`=>` 51992 = 54 . 51988 ≡ 06252 ≡ 0625 ( mod 10000 )
`=>` 4 chữ số tận cùng của 51992 là 0625.
b, 5A = 52 + 53 + 54 + 55 + . . . + 597
5A - A = 4A = 597-5
A = `5^97` − `5^2` A = `5^97` − `5^2`
Mà 597 - 5 = (54)24 . 5 - 5 = 062524 . 5 - 5 = ( . . . 0625) . 5 - 5 = ( . . . 3125 ) - 5 = ( . . . 3120 )
`=>` S = ( . . . 3120 ) : 2
`=>` S = ( . . . 0 )
