Question

What is the remainder when $3^{444}+4^{333}$ is divided by 5?

• A. 1
• B. 2
• C. 4

Answer 1

The dividend is in the form $a^x+b^y$. We need to change it ito the form $a^n+b^n$.
$3^{444}+4^{333}=(3^4{)}^{111}+(4^3{)}^{111}.Now(3^4{)}^{111}+(4^3{)}^{111}=(81{)}^{111}+(64{)}^{111}$ and it will be divisible by $3^4+4^3=81+64=145$.
Since the number is divisible by 145, it will certainly be divisible by 5. Hence, the remainder is 0.