Can someone explain what a conjecture is in math and please provide an example?
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A conjecture is basically a smart guess or a prediction that mathematicians make based on some patterns they’ve noticed. It’s like saying, “I think this is how it works, but I’m not 100% sure yet.”
For example: Imagine you keep adding up the numbers 1, 2, 3, and so on. You notice that the sum (total) always seems to be a multiple of 3. So, your conjecture could be that the sum of any consecutive numbers like 1 + 2 + 3 + … is always a multiple of 3. It’s not proven yet, but you have a hunch that it might be true.
That’s a conjecture in math!
Simply put, a conjecture is a proposition in mathematics that is accepted as true, but not proven.
A famous example is Goldbach’s conjecture, one of the oldest unsolved problems. It says that every even natural number greater than 2 is the sum of two prime numbers. Nobody has ever found a counterexample, so it’s accepted as true, but nobody has ever proved it either.
Another famous conjecture is now called Fermat’s Last Theorem because it has now been proven, but remained unproven for centuries until it was finally proved in 1995, over 350 years later. The theorem says that there are no three positive integers a, b, and c that satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2.
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