give the answer of this question
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If a is a positive integer then according to Euclid law
a = bq+r. ( 0≥r>b )
let take b = 3
a = 3q+r. ( 0≥r>3 )
then value of r is
r = 0,1,2
_______________________
if r = 0
a = 3q+r
a = 3q
______________________
if r = 1
a = 3q+r
a = 3q+1
_____________________
square of the numbers
1) a = (3q)²
a = 3q²
a = 3m. (here m is any positive integer and m = q² )
________________________________________
2) a = (3q+1)²
a = (3q)²+(1)²+2(3q)(1)
a = 9q²+1+6q
a = 9q²+6q+1
a = 3(q²+2q)+1.
a = 3m + 1. (here m is any positive integer and m = q²+2q)
______________________________________________
a = bq+r. ( 0≥r>b )
let take b = 3
a = 3q+r. ( 0≥r>3 )
then value of r is
r = 0,1,2
_______________________
if r = 0
a = 3q+r
a = 3q
______________________
if r = 1
a = 3q+r
a = 3q+1
_____________________
square of the numbers
1) a = (3q)²
a = 3q²
a = 3m. (here m is any positive integer and m = q² )
________________________________________
2) a = (3q+1)²
a = (3q)²+(1)²+2(3q)(1)
a = 9q²+1+6q
a = 9q²+6q+1
a = 3(q²+2q)+1.
a = 3m + 1. (here m is any positive integer and m = q²+2q)
______________________________________________
Apshrivastva:
what about the third remainder
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0
see the attachment for the answer
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