Question

Divisibility ?

Answer 1

`n_1 = 12132` and `n_2 = 12636`

Explanation:

A number `n` is divisible by `4` when the number formed by its two right digits is divisible by `4` and the same number `n` is divisible by `9` when the sum of its digits is divisible by `9`.

We have

`c_1->3 xx 10 + diamond = 4 xx k_1`
`c_2->1+2+square+3+diamond = 9 xx k_2`

here `{square,diamond} in {0,1,2,3,4,5,6,7,8,9}`

From `c_1-> diamond in {2,6}`

Choosing `diamond = 2` we have `c_2->6+2+square_1=9 xx k_3`
so `square_1=1`

Choosing `diamond = 6` we have `c_2->6+6+square_2=9 xx k_4`
so `square_2 = 6`

The solutions are `n_1 = 12132` and `n_2 = 12636`