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MattcAnderson · 2017-04-25, 14:12

Hi Mersenneforum,

With respect to exercise 94,

94. Show that every function from $Z/3Z$

to itself can be specified using a
polynomial of degree at most 2
(or the zero polynomial).

I want to clarify, when you write that we
want a function 'to itself' we can assume that
The domain and the range are the same set?

For example suppose f(0)=0, f(1) = 1 and f(2) = 1.
This would not meet the criterion for exercise 94,
right?

I assume the domain is {0,1,2} and the range is the same.

I see '3 choose 2' or 6 cases that need to be considered for 94.

Thank you, Nick for taking the time to write this up and put it on the internet.

Regards,
Matt

2017-04-25, 14:12	#5
MattcAnderson "Matthew Anderson" Dec 2010 Oregon, USA 3×13×17 Posts	Hi Mersenneforum, With respect to exercise 94, 94. Show that every function from $Z/3Z$ to itself can be specified using a polynomial of degree at most 2 (or the zero polynomial). I want to clarify, when you write that we want a function 'to itself' we can assume that The domain and the range are the same set? For example suppose f(0)=0, f(1) = 1 and f(2) = 1. This would not meet the criterion for exercise 94, right? I assume the domain is {0,1,2} and the range is the same. I see '3 choose 2' or 6 cases that need to be considered for 94. Thank you, Nick for taking the time to write this up and put it on the internet. Regards, Matt Attached Thumbnails Last fiddled with by MattcAnderson on 2017-04-25 at 14:17 Reason: not good ta TEK, I didn't count cases right.