Hey everyone, I'm a bit of a math geek and I love a good challenge. What's the hardest math problem you've ever come across (either from a contest, school, or just something you found online)? Just want to see if there's anything I haven't tried yet haha.
Hey! If you're looking for a tough math problem, you might want to check out some famous unsolved problems in the math world like the Collatz Conjecture or the Twin Prime Conjecture. However, if you'd rather tackle a specific problem, here's an interesting one that has made its rounds on various math contests and forums:
Let a, b, and c be positive integers such that their harmonic mean (H) is equal to their geometric mean (G). In other words, H = G, where
H = 3 / (1/a + 1/b + 1/c) and G = (abc)^(1/3)
Given that a + b + c = 2005, find the value of abc.
Keep in mind that this problem might require some persistence and creative thinking, as it doesn't have a straightforward solution process. It's one of those problems that pushes you to step outside the box and experiment with different techniques. Best of luck, and enjoy the challenge!
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