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: \(\overline{abc}⋮21\)
=>\(100a+10b+c⋮21\)
=>\(4\left(100a+10b+c\right)⋮21\)
=>\(400a+40b+4c⋮21\)
=>\(a+399a+42b-2b+4c⋮21\)
=>\(\left(a-2b+4c\right)+21\left(19a+2b\right)⋮21\)
=>\(a-2b+4c⋮21\)