Consider the eight-digit bank identification number a1a2.…a8, which is followed by a ninth...

Consider the eight-digit bank identification number a1a2.…a8, which is followed by a ninth check digit a9 chosen to satisfy the congruence

(a) Obtain the check digits that should be appended to the two numbers 55382006 and 81372439.

(b) The bank identification number 237a4 18538 has an illegible fourth digit. Determine the value of the obscured digit.