Number theory problem divisible

  • Thread starter yeland404
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  • #1
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Homework Statement



Prove that n ℂ Z+ is divisible by 3( respectively 9). to show that if and only if the sum of its digits is divisible by 3

Homework Equations





The Attempt at a Solution



so n= 3q, q>3 that n[itex]\equiv[/itex]0 mod 3
n=X1* 10^n+ x2*10^n-1......Xn
so need to prove(x1+x2+......Xn)[itex]\equiv[/itex]0 mod 3, the how to prove the next step
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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Homework Statement



Prove that n ℂ Z+ is divisible by 3( respectively 9). to show that if and only if the sum of its digits is divisible by 3

Homework Equations





The Attempt at a Solution



so n= 3q, q>3 that n[itex]\equiv[/itex]0 mod 3
n=X1* 10^n+ x2*10^n-1......Xn
so need to prove(x1+x2+......Xn)[itex]\equiv[/itex]0 mod 3, the how to prove the next step

Show 10^k=1 mod 3.
 
  • #3
Deveno
Science Advisor
908
6
and for extra credit, google "casting out nines" for a better explanation of why this works (the same theorem holds for the number 9, in fact, for the same reason).
 

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