Question

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

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

Hint:

For expressions involving powers, check the divisibility properties of smaller powers and apply them to larger expressions.

Answer 1

The Correct Option is D

We can apply properties of powers and divisibility. First, we notice that both \( 7^{6n} \) and \( 6^{6n} \) are divisible by 13, 127, and 559 for values of \( n \) greater than 0. Therefore, the expression \( 7^{6n} - 6^{6n} \) is divisible by all three values. Thus, the Correct Answer is "All of these".