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(Discrete Math) A routing transit number (RTN) is a bank code that appears in the bottom...

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Advance Math

(Discrete Math) A routing transit number (RTN) is a bank codethat appears in the bottom of checks. The most common form of anRTN has nine digits, where the last digit is a check digit. If d1d2. . . d9 is a valid RTN, the congruence 3(d1 + d4 + d7) + 7(d2 + d5+ d8) + (d3 + d6 + d9) ? 0 (mod 10) must hold.

(a) Show that the check digit of the RTN can detect all singleerrors.

(b) Determine which transposition errors an RTN check digit cancatch and which ones it cannot catch.

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