Question

Let $N={55}^3+{17}^3-{72}^3.$ N is divisible by:

• A. both 7 and 13
• B. both 3 and 13
• C. both 17 and 7
• D. both 3 and 17

Answer 1

The correct option is D both 3 and 17

$N={55}^3+{17}^3-{72}^3=(55+17)({55}^2+{17}^2-55\times 17)-{72}^3=72({55}^2+{17}^2-55\times 17-(55+17{)}^2)$

$=72(-55\times 17-2\times 55\times 17)=-72\times 3\times 55\times 17$.

Hence, the correct answer is option (d).