Congruence in Z(integers) mod n

  • Thread starter capsfan828
  • Start date
  • #1

Homework Statement



In Z mod 5, compute (a + b)5.


Homework Equations





The Attempt at a Solution



Noticing that (a+b)5 = a5+5(a4*b+2*a3*b2+2*a2*b3+a*b4)+b5. Since 5=0 in Z mod 5, it follows that 0(a4*b+2*a3*b2+2*a2*b3+a*b4)=0 and hence (a+b)5=a5+b5.

I am just wondering if it is correct for me to say 5=0 in Z mod 5 and just substitute 0 in for 5?
 

Answers and Replies

  • #2
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[tex]\equiv[/tex]Sounds reasonable to me. Why don't you test this with a couple of numbers to see if your results are consistent with what you've found?

BTW, instead of saying 5=0 in Z mod 5, you can say 5 [itex]\equiv[/itex] 0 mod 5. That 3-bar equals sign means "is equivalent to".
 
  • #3
thanks for the response, much appreciated
 

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