I just asked Chat GPT 3.5 the following: "Please give an exponential equation that has integer solutions which is difficult to solve.", and the response is:
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Certainly, here's an exponential equation that can be challenging to solve for integer solutions:
2^x+3^y=7^z
This equation involves three variables, x, y, and z, and requires finding integer values for these variables that satisfy the equation. This type of equation is known as a Diophantine equation, and solving it can be quite challenging, especially for larger values of x, y, and z.
I mean, it's definitely not a Diophantine equation and solving it is definitely not challenging -- (2, 1, 1) happens to be an easy solution -- but I want to say it probably doesn't have any other solutions but I don't see a great way to prove it...
Certainly, here's an exponential equation that can be challenging to solve for integer solutions:
2^x+3^y=7^z
This equation involves three variables, x, y, and z, and requires finding integer values for these variables that satisfy the equation. This type of equation is known as a Diophantine equation, and solving it can be quite challenging, especially for larger values of x, y, and z.
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