Question

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

Answer 1

Answer:

a=bq+r

b=5

so,

a=5q+r

a=5q, 5q+1, 5q+2, 5q+3, 5q +4

therefore,

a=5q+1

squaring both side

(a)²=(5q)²

a²=25q²

a²=5(5q²)

a²=5q

then

a=5q+1

squaring both side

(a)²=(5q+1)²

a²=25q²+1+10q

a²=5(5q²+2q)+1

a²=5q+1

now

a=5q+2

squaring both side

(a)²=(5q+2)²

a²=25q²+4+20q

a²=5(5q²+4q)+4

a²=5q+4

Answer 2

Answer:

here is the best answer in the pic