4 (a) Write out the multiplication table for Z6. How many times does [0]6 appear in each row of the table? (b) Based on your answer to part (a) (and other examples, if it helps), write down a formula for how many times [0] appears in the [a]m row of the multiplication table for Zm, for any integer a and natural number m. Can you explain why your formula works?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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8
4
(a) Write out the multiplication table for Z6. How many times does [0]6 appear in
each row of the table?
(b) Based on your answer to part (a) (and other examples, if it helps), write down a
formula for how many times [0] appears in the [a]m row of the multiplication
table for Zm, for any integer a and natural number m. Can you explain why your
formula works?
Transcribed Image Text:4 (a) Write out the multiplication table for Z6. How many times does [0]6 appear in each row of the table? (b) Based on your answer to part (a) (and other examples, if it helps), write down a formula for how many times [0] appears in the [a]m row of the multiplication table for Zm, for any integer a and natural number m. Can you explain why your formula works?
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