Question

$7^{6n}-6^{6n},$ where n is an integer $>0$, is divisible by: (CAT 2002)

• A. 13
• B. 127
• C. 559
• D. All of these

Answer 1

The correct option is D All of these

For $n=1,7^6-6^6=(7^3{)}^2-(6^3{)}^2;$

$=(7^3-6^3)(7^3+6^3)=(343-216)(343+216)=127\times 559=127\times 13\times 43.$ Hence it is divisible by $127,13,559.$