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2015-09-26T10:42:26+05:30

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Assume the three consecutive integers as :-
                
      → n , n + 1 and n + 2 respectively 

If suppose any number is divided by 3 , then it's remainder will be either 0 ,1 or 2 .

According to Euclid's algorithm-
     
            a= bq+r { where ''a'' is n , ''b''  is 3 and ''r'' will be less than 3

Hence , for the three consecutive integers we get as follows - 

n=3p+0 = 3p  

n=3p+1  

n=3p+2

If suppose n = 3 p - Then
 
                ''n'' will be divisible by 3  
    
→ If suppose n = 3 p + 1 - Then ,
 
               n+2= 3p +1 +2
    
                           =  3p + 3
          
                           = 3 ( p + 3) → Which is divisible by 3

If suppose n = 3 p + 2 , Then ,
 
             n+1= 3p+2+1
 
                         = 3p+3
 
                         = 3(p+1) → Which is divisible by 3

Hence it is proved that one of every three consecutive integer ( i.e n , n + 1 ,     n + 2 ) is divisible by 3.


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