Question

Prove that the square of any positive integer is of the form 5q, 5q + 1, 5q + 4 for some integer q.

Help me folks. ​

Answer 1

Answer:

let X be any positive intege

then, x=5q or x=5q+1or 5q+4 for integer x

if x =5q

x2=(5q)2=25q2=5(5q2)=5n

Where n= 5q2

if x=5q+1

x2=(5q+1)2 =25q2+10q+1=5(5q2+2q)+1=5+1

were n=5q2+2q

if x=5q+4

x2=(5q+4)2=25q2+40q+60=

5(5q2+8q+3)+1=5+1

were n =5q2+8q+3

therefore in each three cases x2 is either of the form 5q or 5q+1 or 5q+4 and for integer q

Step-by-step explanation:

I hope it is helpful for you