Question

prove that the square of any positive integer is in the of 5q,5q+1, 5q+4 for some integer q

Answer 1

Hey friend.....
Here is your answer

Let a and b are two positive integers.
From Euclid division algorithm,
a=bq+r , where 0<=r<b
According to the question, b= 5
Possible remainder= 0,1,2,3,4
R= 0 a= 5q+0=5q
R=1 a=5q+1
R=2 a=5q+2
R=3 a=5q+3
R=4 a=5q+4
Therefore,positive integers are 5q,5q+1 or 5q+4.

Answer 2

Answer:

I have given you answer in the pic