Answers

  • SRN
  • Helping Hand
2015-07-05T15:49:17+05:30
According to euclid division lemma
a=bq+r
here,b=3
so,r=0
r=1
r=2
when,r=0
let x=3q+0
x^2=(3q)^2 =3(3q^2)
let,m=3q^2
x=3m .............(1)

let,r=1
x=(3q+1)
x^2=(3q+1)^2
x^2=9q^2+6q+1 =3(3q^2+2q)+1
let,m=3q^2+2q
x^2=3m+1 ......(2)

let ,r=2
x=3q+2
x^2=(3q+2)^2
=9q^2+12q+4
=9q^2+12q+3+1
=3(3q^2+4q+1)+1
let ,m=3q^3+4q+1
x^2=3m+1......(3)
from (1),(2),(3),
the square of any positive integer is of the form 3m or3m+1 but not 3m+2....

Hope it'll help you to understand....
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