Question

And b are two positive integers such that the least prime factor of 83 and the least prime factor of b is 5 then calculate the least prime factor of a + b

Answer 1

   

The answer is 2, you could only find the answer easily by supposing a = 83 and b = 5!!! The least numbers having least prime factors 83 and 5 are 83 and 5 themselves respectively. So that a + b = 85 + 3 = 88, whose least prime factor is 2. Or let me show you another thing:

The numbers having the least prime factor 83 and 5 each are in the form 83ⁿ  and 5ⁿ respectively, for any positive integer n. As 83 and 5 are odd, so are 83ⁿ and 5ⁿ. And we know that the sum of two odd numbers is even, so that 83ⁿ + 5ⁿ is even, and it is always true that the least prime factor of every positive even integers is 2. Therefore, so has 83ⁿ + 5ⁿ. That's all!!!

Pls ask me if you have any doubt on my answer. Thank you...