The set of equivalence classes Zn = {[0], [1], - - · , [n – 1]} is an example of what is ... called a finite ring (which simply means the elements can be added and multiplied in familiar ways). (Def.) Two non-zero elements a and b in a ring are called zero divisors if a·b = 0. For example, in Z12 the elements [2] and [6] are zero divisors. Prove the following theorem. Theorem. If n is composite, then there exists at least one pair of zero divisors in Zn.
The set of equivalence classes Zn = {[0], [1], - - · , [n – 1]} is an example of what is ... called a finite ring (which simply means the elements can be added and multiplied in familiar ways). (Def.) Two non-zero elements a and b in a ring are called zero divisors if a·b = 0. For example, in Z12 the elements [2] and [6] are zero divisors. Prove the following theorem. Theorem. If n is composite, then there exists at least one pair of zero divisors in Zn.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The set of equivalence classes Zn = {[0], [1], - - · , [n – 1]} is an example of what is
...
called a finite ring (which simply means the elements can be added and multiplied in familiar
ways).
(Def.) Two non-zero elements a and b in a ring are called zero divisors if a·b = 0. For example,
in Z12 the elements [2] and [6] are zero divisors. Prove the following theorem.
Theorem. If n is composite, then there exists at least one pair of zero divisors in Zn.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcbeb3b9d-7ba5-42f3-adbc-30ae1fc74e26%2F31d5e015-5d84-460c-8a47-bd39e8324559%2Fcv12nvh_processed.png&w=3840&q=75)
Transcribed Image Text:The set of equivalence classes Zn = {[0], [1], - - · , [n – 1]} is an example of what is
...
called a finite ring (which simply means the elements can be added and multiplied in familiar
ways).
(Def.) Two non-zero elements a and b in a ring are called zero divisors if a·b = 0. For example,
in Z12 the elements [2] and [6] are zero divisors. Prove the following theorem.
Theorem. If n is composite, then there exists at least one pair of zero divisors in Zn.
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