5. $T=\sqrt{(2021+2021)+(2021-2021)+(2021 \times 2021)+(2021 \div 2021)}$. What is the largest prime factor of $\mathrm{T}$ ?
SOLUTION
337

Let $x=2021$. Then $T=\sqrt{2 x+x^{2}+1}=x+1=2022$.
Since $2022=2 \times 3 \times 337$, the largest prime factor of $T$ is 337 .