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prove:

n^3-n is divisible by 3

 Sep 8, 2020
 #1
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+1

 

prove:

n^3-n is divisible by 3    

 

                                                               n3 – n 

 

Factor out an n                                      (n) • (n2 – 1)  

 

Factor n2 – 1                                          (n) • (n + 1) • (n – 1)  

 

Rearrange terms                                     (n – 1) • (n) • (n + 1)  

 

Note that the expression consists of three consecutive integers.  

 

When you have three consecutive integers, one of them will be divisible by 3. 

 

If one of the multipliers is divisible by three, then the product is divisible by 3.  

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 Sep 8, 2020
 #2
avatar+332 
+1

tysm for the explanation 

xxJenny1213xx  Sep 8, 2020
 #3
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That is a really neat proof!   Thanks guest.

Melody  Sep 9, 2020

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