Who's up for some math problems?

[lestatdark]

TheLivingShadow said:

lestatdark said:

TheLivingShadow said:

vlad321 said:

So I have only seen Calculation done in this thread, not actual math. Here's a nice eas warm up question:

Let U be a subspace of a finite-dimensional vector space V. Show that if dim(U) = dim(V) then U = V.

 

 I'm sorry, but I don't understand what you're asking. I haven't seen vector space stuff yet. I'll let another person answer this.

For my prior problem, the guy who said the answer was 10⁹ is almost right, but since the problem is M/N and not N/M the actual answer is 1/10⁹. However, it's awesome that you were able to do it congratulations!

Here's a math problem like vlad requested. Even I do not yet know the complete answer to it but I should know in a few days. It should also be noted that I could very easily get the answer with a calculator but that's not the point. Try being true and do it without a calculator. Here's the problem.

Find 4 prime numbers below 100 which are factors of  3³²-2³².

Good luck!

1, 5, 13, 97

 

Please, support your answers with correct mathematical procedure.

Besides that, 1 is not a prime number. It's a special number that's neither prime nor composed.

I'll be waiting for your interesting solution!

 

Ok, i don't know if this procedure is the most viable, but knowing that 3³² - 2³² is an operation with mathematical powers that have different bases, it cannot be done directly, so in the first step, you simply each power and then calculate the resulting subtraction, in which case we get

3³² - 2³² = 1853015893884545

In this scenario, we clearly see 5 as a factor to this operation, given that any number that ends in 5 and 0 is divisable by 5

Then you begin the factorization process by using 5, which will get you

1853015893884545/5 = 376603178776909

If you keep on factoring this number using only prime number, you'll find that the next one is going to be 13, thus

376603178776909/13 = 28507936828993

Repeating the step above, the next prime factor will be 17 (the one that i missed before), so

28507936828993/17 = 1676937460529

Thus for the last number, the same step once again, finding that 97 is the last prime number factor below 100 in 3³² - 2³²

1676937460529/97 = 17288015057

I know it's a crude way to solve this problem, but it was the only one i could think of ;)

Now i have a question for you.

Can you find me the first derivative of the Arctan(x² + x) equation?