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23. Show that if n is not a prime, then there exist [a] and [b] in Z, such that [a] [0] and [b] + [0], but [a] [b] = [0]; that is, zero divisors exist in Z, if n is not prime.

23. Show that if n is not a prime, then there exist [a] and [b] in Z, such that [a] [0] and [b] + [0], but [a] [b] = [0]; that is, zero divisors exist in Z, if n is not prime.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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their own multiplicative inverses. 23. Show that if n is not a prime, then there exist a and [b] in Z, such that [a + 0] and [b] + [0], but [a] [b] = [0]; that is, zero divisors exist in Z, if n is not prime. %3D 24. Let p be a prime integer. Prove the following cancellation law in Zp: If [a] [x] = %3D thon Cnl - 1
Transcribed Image Text:their own multiplicative inverses. 23. Show that if n is not a prime, then there exist a and [b] in Z, such that [a + 0] and [b] + [0], but [a] [b] = [0]; that is, zero divisors exist in Z, if n is not prime. %3D 24. Let p be a prime integer. Prove the following cancellation law in Zp: If [a] [x] = %3D thon Cnl - 1
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