Question

Help me solve this problem

Plss as fast as possible

Answer 1

Let p be m
let ' a' be any positive integer and b = 3.
we know, a = bq + r , 0 <  r< b.
now, a = 3q + r , 0<r < 3.
the possibilities of remainder = 0,1 or 2
Case I - a = 3q
a2 = 9q2
  = 3 x ( 3q2)
  = 3m (where m = 3q2)
Case II - a = 3q +1
a2 = ( 3q +1 )2
  =  9q2 + 6q +1
  = 3 (3q2 +2q ) + 1
  = 3m +1 (where m = 3q2 + 2q )
Case III - a = 3q + 2
a2 = (3q +2 )2
    = 9q2 + 12q + 4
    = 9q2 +12q + 3 + 1
  = 3 (3q2 + 4q + 1 ) + 1
  = 3m + 1 where m = 3q2 + 4q + 1)

if you want substitute p in the place of m