Question

If \( u, v, w \) and \( m \) are natural numbers such that \( u^m + v^m = w^m \), then which one of the following is true?

• A. \( m \geq \min(u, v, w) \)
• B. \( m \geq \max(u, v, w) \)
• C. \( m<\min(u, v, w) \)
• D. None of these

Hint:

Use Fermat's Last Theorem to recognize that such equations do not hold for integers when \( m>2 \).

Answer 1

The Correct Option is D

The equation \( u^m + v^m = w^m \) is a generalized form of Fermat's Last Theorem, which tells us that there are no integer solutions to this equation for \( m>2 \). Therefore, none of the given options are true. Thus, the Correct Answer is "None of these".