N = 55^{5} + 17^{5} – 72^{5}
N = (54 + 1)^{5} + (18 - 1)^{5} – 72^{5}
The above is divisible by 3
N = (51 + 4)^{5} + 17^{5} – (68 + 4)^{5}
The above is divisible by 17
N = 55^{5} + (11 + 6)^{5} – (66 + 6)^{5}
The above is divisible by 11
N cannot be expressed in favourable of 7 and 13 and hence is not divisible by 7 and 13
From the above the best answer choice is (B) – N is divisible by both 3 and 17
Correct Answer: Choice B