Question

Find the smallest prime number dividing the sum 3¹¹ + 5¹³.

Answer 1

Answer:

2

Step-by-step explanation:

Any product of odd numbers is always odd.

The sum of two odd numbers is always even.

Since, 3`11 and 5`13 are both the product of odd numbers, so they are both odd

So 3`11 + 5`13 is the sum of two odd numbers and is therefore even.

Any even number is divisible by 2. Therefore 2 is the smallest prime that divides 3`11 + 5`13

Also,  3`11 + 5`13 = 1220880272

Therefore, the smallest prime number dividing the sum 3¹¹ + 5¹³ is 2.

Answer 2

Answer:

Step-by-step explanation:

3`11=177147. and 5`13=1220703125. 3`11+5`13=177147+1220703125.

=1220880272

The sum of odd numbers is even. We have 2 in units place. It can be divided by 2 . Which is a smallest prime number.