Notices by 🎓 Dr. Freemo :jpf: 🇳🇱 (freemo@qoto.org), page 106

@Deepsealioness ::raises hand:: hope you are doing well.

@khird agreed

@khird A slightly different wording, but 100% valid all the same, good job :)

For those who arent on an instance with math rendering you can read the answer here: http://mathb.in/38503

In the language of math the key is in how we frame the question. For example the following will provide some insight as I will show in a momemt.

\(\exists n \in \mathbb{N}\) such that \(n^3 - 1\) is prime

Not everyone understands the above notation so let me rephrase it more simply. The above translates to "There exists a Natural Number, \(n\), such that \(n^3 - 1\) is prime." Remember a Natural Numer is any positive Integer. In this example assuming that the original assertion that "8 is the only perfect cube to follow a prime" then \(n = 2\) which means the prime number, \(7\), is \(2^3 - 1 = 7\), and \(8\) is just \(2^3 = 8\). Easy enough, but how can we prove that this is the only case...

So we really just need to figure out which values for n in the equation above will give us a prime number, then we have our answer. A prime number is any number which only has 1 and itself as its factors. In other words the only two natural numbers we could possibly multiply together to get 7 is 1 and 7. So we have to start by factoring out the above equation \(n^3 - 1\), if we do that we get:

\[(n-1) \cdot (n^2+n+1)\]

It should be immediately obvious that of these two factors the left-most one is the smaller number, so we know:

\[(n-1) < (n^2+n+1)\]

Since we only care about prime numbers which satisfy the equation we know the left hand term must be equal to 1 and the right hand term most be equal to the entire number. So we can likewise assert the following:

\[1 = n-1\]
\[n^3 - 1 = n^2+n+1\]

Now we can use either equation and solve for n. It doesnt matter which equation you solve they will both give you the same value for n. Solving for n we get:

\[n = 2\]

If we plug that into the original equation, as we said earlier, er get the answer of 7, therefore 7 is the only prime number followed by a perfect cube.

\[2^3 - 1 = 7\]

@Absinthe ill provide the answer in a few seconds

@Absinthe Yet humans are the only speciesa that have engorged breasts prior to bearing a baby, not even chimps have that.

@Absinthe What do you mean? We are looking for a perfect cube that follows a prime and proving 8 is the **only** one.

@danie10 There are tons, MS does not prohibit advertisements in their stream. Not sure what gave you the impression MS had no advertisements...

@Absinthe Just because something is harmful doesnt garuntee it would be unattractive, no.

But you are right that the breeding isnt forced, it happens naturally, but it can still be harmful despite this.

One of my favorite math problems that is easy to solve with just algebra:

Prove that 8 is the only perfect cube to follow a prime number.

If you don't know what a perfect cube is, that is simple, it is any integer raised to the power of 3. Since \(8 = 2^3\) it is a perfect cube, and it follows the number 7, which is prime. 8 is the only number that fits those conditions... prove it.

NOTE: I will give the answer as a reply. If anyone else wants to provide an answer please make sure you use a content warning.

#maths #math #mathematics #riddle #puzzle #riddles #puzzles

@Absinthe

Perhaps :)

@mikelga

@Absinthe If a particular gene is harmful then you are better off eliminating it entierly (make sure you dont have even one set) so as to ensure the harmful expression of the gene doesnt crop up later.

@danie10 Ok so its decentralized ads, not sure thats any better. In fact its worse at least with normal ads my ad blocker works.

@Skip Yes just mute the instance (option under the three dots)

Business Idea: Sell shirts soaked in oil and then washed really good. Then when you get food on your shirt and wash it it doesnt leave oil stains because the whole shirt is one big oil stain.

If anyone does this idea I demand royalties!

@cowanon hahah thanks :)

Seems I just hit the 7,000 follower mark.

Thank you to all the new followers!

:nyancat_rainbow::nyancat_rainbow::nyancat_rainbow::nyancat_rainbow::nyancat_rainbow::nyancat_rainbow::nyancat_body::nyancat_face:

Newton was an asshole, team Leibniz!

#Leibniz4Life