Prove that one of every three cosecutive integer is diviseble by 3

1
by chetan281234

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-

{ where ''a'' is n , ''b''  is 3 and ''r'' will be less than 3

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

If suppose n = 3 p - Then

''n'' will be divisible by 3

→ If suppose n = 3 p + 1 - Then ,

=

=  → Which is divisible by 3

If suppose n = 3 p + 2 , Then ,

=

=  → 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.