# Thread: binary & decimal representations of int. - N, M are int, formed by reverse ...

1. ## binary & decimal representations of int. - N, M are int, formed by reverse ...

Bank ID number is 237(a4)18538 and has an illegible 4th digit.
Determine the value of a4.

They also give the check digit formula, so a9 = 7(a1) + 3(a2) + 9(a3) + 7(a4) + 3(a5) + 9(a6) + 7(a7) + 3(a8) (mod 10)

2. Hello, cassiopeia1289!

Bank ID number is: .$\displaystyle 237(a_4)18538$ and has an illegible 4th digit.
Determine the value of $\displaystyle a_4.$

They also give the check-digit formula:
. . $\displaystyle a_9 \:= \:7(a_1) + 3(a_2) + 9(a_3) + 7(a_4) + 3(a_5) + 9(a_6) + 7(a_7) + 3(a_8) \pmod{10}$

Using the check-digit formula:

. . $\displaystyle 8 \:=\:7(2) + 3(3) + 9(7) + 7(a_4) + 3(1) + 9(8) + 7(5) + 3(3) \pmod{10}$

. . $\displaystyle 8 \:=\:7(a_4) + 205 \pmod{10}$

We have: .$\displaystyle 7(a_4) \:=\:\text{-}197 \pmod{10}$

. . . . . . . .$\displaystyle 7(a_4) \:=\:3 \pmod{10}$

. . . . . . . . . $\displaystyle a_4 \:=\:9$

3. awesome, thank you!