Question

Find the smallest prime number dividing the sum $3^{11}+5^{13}$.

Answer 1

The numbers $3^{11}$ and $5^{13}$ are odd numbers as any product of odd numbers is odd and it is known that the sum of two odd numbers is an even number.
An even number is divisible by 2 and 2 is a prime number. So, the smallest prime number that divides $3^{11}+5^{13}$ is 2.