Question

Write 123 as difference of the square of two consecutive natural numbers.

Answer 1

We can write $123$ as,
$123=(61\times 2)+1⟹123=61+61+1=62+61$
If we multiply $62+61$ by $1$ result will not change because 1 is a multiplicative identity.
$⟹123=(62+61)\times 1$
And we can write $1$ as $62-61$,
$⟹123=(62+61)\times (62-61)⟹123={62}^2-{61}^2$