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There is no longest problem. Some problems are very easy to state but require a very long proof. Some are easy to prove )or evaluate) but the answer is very long.
An example of the first is that there is no solution to xn + yn = zn for positive integers x, y and z when n is an integer greater than 2.
On the other hand the ratio, pi = circumference/diameter of a circle has been know for thousands of years. But the exact value of pi cannot be written in any base (other than pi or directly related) is infinitely long.
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What is the most complicated math problem?
There is no "most complicated math problem" because numbers are infinite. However, on very complicated problem is pi=? because pi is a repeating decimal, it would go on forever. Because of that, we usually sorten pi to 3.1415...
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reasoning!!!
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The most complex type of behavior needed solve a difficult math problem?
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