Question

01

Show that square of any positive integer is not in the form of 3m+2 ,where
m is some integer​

Answer 1

Correct Question

• Show that square of any positive integer is in the form of 3m,3m+1 and 3m+2 ,where
• m is some integer

AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• M is a integer

${\sf{\green{\underline{\large{To\:show}}}}}$

• Square of any positive integer
• is in the form of 3m+2

${\sf{\pink{\underline{\Large{Explanation}}}}}$

Let a be any + integer divided by 3 give some remainder ang give some quotient q

a = bq+r

$\tt{bq+r}\begin{cases}r\leq{a} \end{cases}$

R=0,1,2

We have 3 cases

Case 1

when r =0

a=bq+r

=>a=3q

Case-2

when r=1

a=bq+r

a=3q+1

Case-3

when r=2

a=bq+r

a=3q+2

Hence,any + integer is in the form of 3m,3m+1 and 3m+2