Question

chứng minh(100xa+10xb+c)chia hết cho 21 biết (a-2b+4c)chia hết cho 21

Answer 1

\(4\left(100a+10b+c\right)=400a+40b+4c\)

\(=a-2b+4c+399a+42b\)

\(=\left(a-2b+4c\right)+21\left(19a+2b\right)\)

\(a-2b+4c⋮21;21\left(19a+2b\right)⋮21\)

=>\(a-2b+4c+21\left(19a+2b\right)⋮21\)

=>\(4\left(100a+10b+c\right)⋮21\)

=>\(100a+10b+c⋮21\)