7⁶ⁿ– 6⁶ⁿ, where n is an integer >0, is divisible by
a) 13
b) 127
c) 559
d) All of these

Answer: d
Explanation:
$$\eqalign{ & {7^{6n}} – {6^{6n}} \cr & = {7^6} – {6^6} \cr & = {\left( {{7^3}} \right)^2} – {\left( {{6^3}} \right)^2} \cr & = \left( {{7^3} – {6^3}} \right)\left( {{7^3} + {6^3}} \right) \cr & = \left( {343 – 216} \right) \times \left( {343 + 216} \right) \cr & = 127 \times 559 \cr & = 127 \times 13 \times 43 \cr} $$
Clearly, it is divisible by 127, 13 as well as 559