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For any positive integer a and 3, there exist unique integers q and r such that a = 3q + r, where r must satisfy?

a=bq+r where, 0 ≤ r

r

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F

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Possible value of r= 0,1,2 And the possible value of a is as- When r=0 a= 3q+0 a=3q When r=1 a= 3q+1 When r=2 a=3q+2 Hence these above are the required possible values of a and r
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for any posit8very interger

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a = 3q + r

Euclid division lemma  a=bq+r    
any number can be represented in this form 
where  0 ≤ r <  b   

Comparing a = 3q  + r   wirh  a  = bq + r
=> b = 3 
Subtitling b = 3 in 0 ≤ r <  b 
we get  0 ≤ r <  3 

Hence r can be 0 , 1  , 2   or   0 ≤ r <  3 
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