Question

Find the smallest prime divisor of 5^23+7^17?

Answer 1

LOL !!
5 * 7

Answer 2

well, both numbers are odd, so their sum will be even.
2 is the smallest prime divisor.

Answer 3

sorry, missed the plus sign. oobleck is right

Answer 4

In order to systematically do it, find the the units digit of each term, for 5^23, it’ll be 5, and for 7^17, it’ll be 7 (can be found through finding the pattern of units digits for powers of 7). If you add these two, you’ll get a units digit of 2, which tells you the number is divisible by 2 always.

Answer 5

We see the last digit of the 5^23 is 5 always.
The last digit of 7^17 followed the sequence 7, 9, 3, 1, 7, ... so every multiple of 4 exponents, its last digit will be 1, so 7^17 = (7^16)*7 have 7 as it last digit.
The sum 5 + 7 for the last digit is 2 thus the smallest prime divisor is 2.