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Discrete Maths

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FallonXay:

--- Quote from: RuiAce on April 22, 2017, 10:09:47 pm ---

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x = 1 doesn't give 0 though? So would you just do a proof by cases? (Test, 0, 1, 2, 3 mod4)?

Also, for part a, how come you can just substitute it in? Is that just a property of congruency?

Thanks!

RuiAce:

--- Quote from: FallonXay on April 23, 2017, 07:32:16 am ---x = 1 doesn't give 0 though? So would you just do a proof by cases? (Test, 0, 1, 2, 3 mod4)?

Also, for part a, how come you can just substitute it in? Is that just a property of congruency?

Thanks!

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My bad, I think I messed up some of my mental arithmetic because it would be 2 mod 4.
In that case, upon exhausting all the cases we see that the converse is true.

Yes, you were taught several properties of congruence back in topic 2.

FallonXay:

--- Quote from: RuiAce on April 21, 2017, 02:17:42 pm ---



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Heyy, just looking over this proof.  In this line:

--- Quote from: RuiAce on April 21, 2017, 02:17:42 pm ---

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How come it's 'a' to the power of 'k' to the power of '(m-1)'. Don't we just substitute 'km' into the place where there was originally an 'n' to give k to the power of (km - 1)?

Also, could you clarify this section? I'm a little confused as to what's happening here:


--- Quote from: RuiAce on April 21, 2017, 02:17:42 pm ---

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Thanks!  :)

RuiAce:

--- Quote from: FallonXay on April 23, 2017, 12:24:08 pm ---Heyy, just looking over this proof.  In this line:
How come it's 'a' to the power of 'k' to the power of '(m-1)'. Don't we just substitute 'km' into the place where there was originally an 'n' to give k to the power of (km - 1)?

Also, could you clarify this section? I'm a little confused as to what's happening here:

Thanks!  :)


--- End quote ---
That last one had typo's in it. One of those k's should've been a 1 and the other an m. Fixed in the original post.
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FallonXay:
Question 2 of Discrete Exam Working Out

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