Question

Find whether the square of the following numbers are even or odd?
$17779$

Answer 1

here $17779=(17780-1)$

now square of $a-b$ can be written as $a^2-2ab-b^2$

So, $(17779{)}^2=(17780-1{)}^2$

$=(17780{)}^2-2(17780\left)\right(1)+(1{)}^2$

$\to$ now any even number square became even only.

$\to$ even multiply even number convert it self even.

$\to$ here $(1{)}^2$ will be odd number

So, $(17779{)}^2\Rightarrow EVEN-EVEN+ODD$

$\to$ here $EVEN+EVEN=EVEN$

$EVEN+ODD=ODD$

$ODD+ODD=EVEN$

So, $(17779{)}^2=EVEN-EVEN+ODD$

$EVEN+ODD$

$(17779{)}^2=ODD$