Question

Show that the square of positive integer is of the form 5q+2 or 5q+3 for any integer q.

Answer 1

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→ Show that the square of any positive integers cannot be of the form 5q+2 or 5q+3 for any integer q.

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Answer 2

$\huge \bf{ \red{hey}}$

$\huge{ \mathfrak{here \: is \: answer}}$

let a be any positive integer

then

b=5

0≤r<b

0≤r<5

r=0,1,2, 3,4

case 1.

r=0

a=bq+r

5q+0

5q

case 2.
r=1
a=bq+r

5q+1

case 3.

r=2

5q+2

case4.

r=3
5q+3

case 5.

r=4

5q+4

from above it is proved.

$\huge \boxed{ \boxed{ \pink{hope \: it \: helps}}}$

$\huge{ \green{thanks}}$