Question

Cho A =999993¹⁹⁹⁹-555557¹⁹⁹⁷.   Chứng minh A chia hết cho 5

Answer 1

Ta có :

A=999993^{1999}-555557^{1997}A=9999931999−5555571997

=999993^{1998}.999993-555557^{1996}.555557=9999931998.999993−5555571996.555557

=\left(999993^2\right)^{999}.999993-\left(555557^2\right)^{998}.555557=(9999932)999.999993−(5555572)998.555557

=\left(.......9\right).999993-\left(......1\right).555557=(.......9).999993−(......1).555557

=\left(....7\right)-\left(....7\right)=(....7)−(....7)

=\left(....0\right)⋮5=(....0)⋮5

\Leftrightarrow A⋮5\left(đpcm\right)⇔A⋮5(đpcm)