Exercise 36. Prove the above theorem. Hint: some pieces have been done in earlier theorems and exercises. For example, if you want to show [0] is the additive identity, you only need to show [a]+[0] = [a] since [0]+[a] = [a]+[0] from an earlier theorem.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Prove Theorem 20.

Theorem 20. Let m be a positive integer. Then Zm is a commutative ring
with additive identity [0] and multiplicative identity [1]. The additive inverse
of (a] is [-a).
Transcribed Image Text:Theorem 20. Let m be a positive integer. Then Zm is a commutative ring with additive identity [0] and multiplicative identity [1]. The additive inverse of (a] is [-a).
Exercise 36. Prove the above theorem. Hint: some pieces have been done
in earlier theorems and exercises. For example, if you want to show [0] is the
additive identity, you only need to show [a]+[0] = [a] since [0]+[a] = [a]+[0]
from an earlier theorem.
Transcribed Image Text:Exercise 36. Prove the above theorem. Hint: some pieces have been done in earlier theorems and exercises. For example, if you want to show [0] is the additive identity, you only need to show [a]+[0] = [a] since [0]+[a] = [a]+[0] from an earlier theorem.
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