Question

Find the smallest prime number dividing the sum 3power11+5power13

Answer 1

Answer:

2

Concept used:

⇒ The all powers of any positive odd integers are also odd.

⇒ The sum of any two odd positive integers is always even.

⇒ The smallest prime number which divides all even positive integers is always 2.

Step-by-step explanation:

⇒ According to the first concept, as 3 and 5 are odd integers, then so are 3¹¹ and 5¹³ respectively.

⇒ According to the second concept, as both 3¹¹ and 5¹³ are odd, then neither is 3¹¹ + 5¹³, which means it is even.

⇒ According to the third concept, 2 is the answer.