Question

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Answer 1

Step-by-step explanation:

The sum of two odd numbers is always even. So 3^11 + 5^13 is the sum of two odd numbers and is therefore even. Therefore, the smallest prime number dividing the sum 3¹¹ + 5¹³ is 2.

Answer 2

Any product of odd numbers is odd.
The sum of two odd numbers is even.

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. [In fact, 2 is the
smallest prime]

[ 3^11 + 5^13 = 1220880272 = 24*47*107*15173, but we don't need that!)
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