Question

prove that the square of any positive integer is of the form 5q,5q+1,5q+4

Answer 1

let any positive integer be in the form of 5m+r
where r=0,1,2,3,4.
let us assume that a=5m+r
let r=0
a=5m+0
on squaring both sides
a^2=25m^2
=5(5m^2)
where 5m^2 = q
a^2=5q ....

hope it helpss

Answer 2

let the positive integer be a= 5q+r
b=5q
where,r=0,1,2,3,4
r=0
a=5q+r
=5q+0
=5q

r=1
a= 5q+r
a=5q+1  (squaring both sides)
=(5q+1)
=5q*5q+1*1
25q+1
5(5q+1)
5q+1
 
R=2
formula = a2 +b2 +2ab
A=5q+r
=5q+2 (s.b.s)
5q*5q+2*2
25q+4
(5q+4)