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Hard math problem

Solve the equation 5^x+6^y+7^z+11^u=1999

How do you solve this? How should you think?
tengil
Solve the equation 5^x+6^y+7^z+11^u=1999

How do you solve this? How should you think?


I assume you are looking for integer solutions.

Brute force.

Start with the highest power of the largest integer (11), subtract that, then repeat with the second largest integer (7).
third and fourth.

Didn't work, decrease the power of the 3rd integer by one and try again....

I got an answer (don't know if it's unique) in about 4 minutes.

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