Question

Answer 1

a: \(\overline{abcd}⋮29\)

=>\(1000a+100b+10c+d⋮29\)

=>\(986a+14a+87b+13b+10c+d⋮29\)

=>\(29\left(34a+3b\right)+14a+13b+10c+d⋮29\)

=>\(14a+13b+10c+d⋮29\)

=>\(-2\left(14a+13b+10c+d\right)⋮29\)

=>\(-28a-26b-20c-2d⋮29\)

=>\(-28a+29a-26b+29b-20c+29c-2d+29d⋮29\)

=>\(a+3b+9c+27d⋮29\)

b: \(\overline{abc}⋮21\)

=>\(100a+10b+c⋮21\)

=>\(4\left(100a+10b+c\right)⋮21\)

=>\(400a+40b+4c⋮21\)

=>\(a+399a+42b-2b+4c⋮21\)

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

=>\(a-2b+4c⋮21\)