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consider the equation n4 m4 = 625. (a) are there any integers n and m that satisfy this equation? prove it.

User Dabljues
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Final answer:

After analyzing the equation n^4 + m^4 = 625, it was determined that there are no integer values of n and m that can satisfy the equation, as shown by setting m=2 and demonstrating that no integer n can be found to satisfy n^4 = 609.

Step-by-step explanation:

To consider the equation n4 + m4 = 625, we look for integer solutions for n and m. We are told to try setting M = 2 in the equation they reference (presumably n or m is represented by M), and then solving for the other variable. If we set m = 2, we would have n4 + 24 = 625. Since 24 is 16, our equation becomes n4 + 16 = 625, or n4 = 609. It is not possible for n to be an integer because 609 is not a perfect fourth power. Therefore, there are no integers n and m that satisfy this equation.

User Greg Terrell
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