Did I just come up with this?

  • Thread starter enkrypt0r
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In summary, the speaker shares that they had a lot of free time last summer and would often play with math and numbers. They stumbled upon what they thought could be a new theorem or axiom, but after researching online, they found that it already exists. The theorem states that if the absolute value of a minus b is equal to one, then the least common multiple of a and b is equal to their product. The speaker admits that it may not be useful, but they are still curious about it. However, it turns out that this statement is simply stating that the least common multiple of two consecutive integers is their product. The speaker is encouraged to continue exploring and discovering new things.
  • #1
enkrypt0r
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Well, last summer I had a lot of time on my hands, and I would stay up late just randomly playing with math and numbers to kill time. After playing around with them long enough, I seem to have come up with a theorem/axiom/postulate (I don't know the terminology). I never really thought that I had come up with anything new until I had a look at my notebook today, and started Googling. Perhaps I wasn't trying the right keywords, but I can't find anything like this online. Now that I think about it, I seem to remember writing a program to prove this true, and it ended up working. I've since reformatted that computer (installed my mom's new OS).

Anyways, it's not really a big deal or anything, and I doubt it's really useful, but:"If the absolute value of a minus b is equal to one, then the least common multiple of a and b is equal to ab."

or

If |a-b| = 1 Then LCM(a,b) = abI'm sure something like this is already in existence, but I can't seem to find it... Can anybody else?
 
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  • #2
I'm afraid what you've come up with isn't new-- your statement says that the least common multiple of two consecutive integers is their product. You can see this by looking at the formula for the least common multiple of two numbers [tex]lcm(a,b)=\frac{ab}{gcd(a,b)}[/tex]. Since a and b are consecutive, gcd(a,b)=1, which yields the result.

Still, carry on playing around on your notebook and one day you'll discover something new!
 

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To "come up with" something means to think of or create something new or original.

2. How can I tell if I actually came up with an idea?

If you can clearly remember the thought process and steps you took to arrive at the idea, it is likely that you came up with it yourself.

3. Is it possible for two people to come up with the same idea independently?

Yes, it is possible for two people to come up with the same idea independently. This is known as parallel thinking or convergent evolution of ideas.

4. What factors can influence the formation of new ideas?

Some factors that can influence the formation of new ideas include personal experiences, exposure to new information or perspectives, and the ability to think creatively.

5. How can I improve my ability to come up with new ideas?

Practicing activities that stimulate creativity, such as brainstorming, keeping an open mind, and exploring new interests and experiences, can help improve your ability to come up with new ideas.

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