Question

State whether True or False:

${13}^3-5^3$ is divisible by $8$

• A. Yes
• B. no
• C. Invalid question
• D. Cannot be determined

Answer 1

The correct option is A Yes

Let $f\left(x\right)=x^n-y^n$
By remainder theorem,, if $f\left(a\right)=0$, then $x-a$ divides $f\left(x\right)$
Thus, $f\left(y\right)=y^n-y^n$
$=0$
Thus, $(x-y)$ divides $x^n-y^n$
Here, given polynomial is ${13}^3-5^3$
$8=13-5$
Comparing it with the above, $x=13$, $y=5$, and $n=3$
Using the above proof, we can say that ${13}^3-5^3$ is divisible by $8$