Soukarya Saha
Last Activity: 7 Years ago
let p be a positive integer such that
a = p2
We know that on dividing a positive integer by 3 we get remainder as either 0,1 or 2 because 0
Using Euclids division lemma,
p=3q
p2=9q2
a=3(3q)
since 3q is any integer, it can be said
a = 3m
Similarly
p= 3q +1
p2= 9q2+6q+1
a= 3(3q2+2q) +1
since (3q2+2q) is any integer
a = 3m+1
again
p = 3q+2
p2= 9q2+12q+4
a = 3(3q2+4q+1) +1
since (3q2+4q+1) is any integer
a = 3m+1
Hope it helps.
