Question

what is the least prime number which is a divisor of 7^9 + 11^25?
(A). 1
(B) 2
(C) 3
(D) 5
(E) 7^9+11^25

Answer 1

Square 7 to get 49. Multiply that by 7 to get 343, and then multiply this by 7 to get 2401. Keep going until you notice a pattern: the units digit will cycle. The cycle is 1,7,9,3. Notice all of these digits are odd. Do the same with 11 and you'll notice that ALL powers of 11 have a units digit of 1 (which is also odd). So basically ANY power of 7 or 11 is going to be odd. Since odd+odd = even, this means that 7^9 + 11^25 is an even number (whatever number this monstrous number is)


So 7^9 + 11^25 is divisible by 2 (ie 2 is a factor). So the answer is B)

Answer 2

Oh I should point out that 1 is NOT a prime number (by definition), so we can throw out answer choice A)