Ta có: \(A=999993^{1999}-555557^{1997}\)
\(=999993^{1998}.999993-555557^{1996}.555557\)
\(=\left(999993^2\right)^{999}.999993-\left(555557^2\right)^{998}.555557\)
\(=\left(...9\right)^{999}.999993-\left(...9\right)^{998}.555557\)
\(=\left(...9\right).999993-\left(...1\right).555557\)
\(=\left(...7\right)-\left(...7\right)\)\(=\left(...0\right)\)
Chữ số tận cùng của \(A=999993^{1999}-555557^{1997}\) là \(0\).
\(\Rightarrow\)\(A=999993^{1999}-555557^{1997}⋮5\)
Cho \(A=999993^{1999}-555557^{1997}\)
Vì \(^{1999}\) có dạng \(4n+3\) nên \(999993^{1999}=\overline{...7}\)
Vì \(^{1997}\) có dạng \(4n+1\) nên \(555557^{1997}=\overline{...7}\)
Ta có: \(\overline{...7}-\overline{...7}=\overline{...0}\)
\(\overline{...0}⋮5\) \(\Rightarrow\) \(A⋮5\)
Ta có: A = 99999 3 1999 − 55555 7 1997 A=999993 1999 −555557 1997 = 99999 3 1998 . 999993 − 55555 7 1996 . 555557 =999993 1998 .999993−555557 1996 .555557 = ( 99999 3 2 ) 999 . 999993 − ( 55555 7 2 ) 998 . 555557 =(999993 2 ) 999 .999993−(555557 2 ) 998 .555557 = ( . . . 9 ) 999 . 999993 − ( . . . 9 ) 998 . 555557 =(...9) 999 .999993−(...9) 998 .555557 = ( . . . 9 ) . 999993 − ( . . . 1 ) . 555557 =(...9).999993−(...1).555557 = ( . . . 7 ) − ( . . . 7 ) =(...7)−(...7) = ( . . . 0 ) =(...0) Chữ số tận cùng của A = 99999 3 1999 − 55555 7 1997 A=999993 1999 −555557 1997 là 0 0. ⇒ ⇒ A = 99999 3 1999 − 55555 7 1997 ⋮ 5 A=999993 1999 −555557 1997 ⋮5
