Bank Account Check Digit (Congruences modulo 10) The identification number for a bank printed on a check consists of eight digits x1 . . . x8, followed by a ninth check digit x9, with x9 ≡ 7x1 +3x2 + 9x3 + 7x4 + 3x5 + 9x6 + 7x7 + 3x8 (mod 10). (a) What is the check digit following the eight-digit identification number 00185403 for a bank? (b) Will this scheme detect a change in one of the digits? Prove your answer. (c) Will this scheme detect a change the transposition of two consecutive, but distinct digits? Prove your answer.

The identification number for a bank printed on a check consists of eight digits x1 . . . x8, followed by a ninth check digit x9, with x9 ≡ 7x1 +3x2 + 9x3 + 7x4 + 3x5 + 9x6 + 7x7 + 3x8 (mod 10). (a) What is the check digit following the eight-digit identification number 00185403 for a bank? (b) Will this scheme detect a change in one of the digits? Prove your answer. (c) Will this scheme detect a change the transposition of two consecutive, but distinct digits? Prove your answer.

Equality of gcd's

Show that if gcd(a, b) = 1, then gcd(ac, b) =gcd(b, c).

The Euler function

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Euler function

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Euler Function

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