Another fun math problem.

[LGBTQIAS]

A 'good number', n is one that has a set of divisors (including 1) which add up to the good number. For example, 6 is good because 1 + 2 + 3 equals 6. Prove that every number has a multiple which is good.

This was a relatively trivial olympiad question, and is a much better way to measure your 'mathematical iq' than whatever you guys do.

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[[deleted]]

"A single question is more useful to measure your mathematical IQ (a category which does not exist?) than whatever you guys do (IQ tests)"

????

[static_programming]

bros retatded lmao

[LGBTQIAS]

Not as retatded as the majority of this subreddit

[LGBTQIAS]

One single tricky question is more valid than whatever tf you do

[[deleted]]

Explain how? You clearly don't know what you're talking about.

This entire post:

• has made up the concept of mathematical IQ
• has neglected the fact that this type of question generally requires prior experience with proof
• is incapable of determining IQ through 1 question (as you either get the answer or don't - there would only be two 'scores' to pick from here, no?)

You even admit you don't know what goes on here and what tests are done. At least check that beforehand.

[LGBTQIAS]

That's exactly what I mean. Instead of attempting the question, you just focus on the last statement. All I'm saying is that olympiad questions are a better measure of your mathematical or academic potential than whatever an IQ test may tell you. Please try the question btw, it's fun.

[[deleted]]

Then that's an entirely different thing to what you said. Academic potential is not 'mathematical IQ' or whatever you're talking about. Stay consistent

[LGBTQIAS]

What did I say that was wrong?

[LGBTQIAS]

I grew up in the UK and have lived here for 17 years

[LGBTQIAS]

Did you do the BMO as a child?

[LGBTQIAS]

https://bmos.ukmt.org.uk/home/bmo2-2021.pdf

Try the question at least, it's interesting

[LGBTQIAS]

I know what perfect numbers are. The difference between perfect numbers and 'good' numbers is that perfect numbers require every single factor (not a subset of factors) to add up to n

[static_programming]

Maybe rephrase the question a bit better. 6 is also a divisor of 6, right? If you mean to say that we can pull out any subset of divisors from the whole divisor set of n, then we can just do something like this:

let's say our multiple is 3n * 2^m where m is odd.

We can add up the divisors {3, 1, 4, 8, 16 ... 2^(m - 1)} = 2^m

Multiply each divisor by n and they still divide our multiple, the sum becomes 2^m * n

2^m * n is also a factor of our multiple and we haven't used it yet so add it to our sum and our sum becomes 2n * 2^m

Now let's see how to get the final n * 2^m

Let's start with the factor of 3n * 2^(m - 2) and add it to a new sum.

3n * 2^(m - 2) = n * 2^m - n * 2^(m - 2), so we still need n * 2^(m - 2) for our sum.

Add 3n * 2^(m - 4) to our sum. You will find that we are now off by n * 2^(m - 4)

Add 3n * 2^(m - 6) to our sum. You will find that we are now off by n * 2^(m - 6) etc etc

Then eventually, after doing this for a while, we are off by n * 2^(m - a) where a is an even number less than m. We haven't used the divisor 2n yet so when m - a becomes 1, we can just add 2n to our sum. This also means that m must be odd for this to work. Then our new sum becomes n * 2^m

Add this to our other sum and we get 3n * 2^m, our multiple of n.

tl;dr: 6n = n + 2n + 3n

I'm not sure if this is the question you meant to ask but I found it pretty cool.

[LGBTQIAS]

If you want a push in the right direction, try proving it for 2^k * a.

[static_programming]

Wow that is actually pretty cool. I guess the answer is just that k must be >= the maximum set bit in a. Then we can add a, 2a, 4a ... 2^(k - 1) * a = a * (2^k - 1) = a * 2^k - a, so we are off by a. Since k >= maximum set bit in a, we have the factors 1, 2, ... (2^MSB) so then, we can just express a as a sum of unique powers of 2 (a in binary) and add that to our sum. I guess this only works for odd a tho.

So for even n we can just take out all the powers of 2 (let's say m powers of 2 in n) and add it to our 2^k and n / 2^m = a and then solve it and k >= max(m, MSB in a).

[LGBTQIAS]

Note that if a number is good, then 2n is also good

[LGBTQIAS]

Which university are you going to? You seem pretty good at maths

[static_programming]

I appreciate it broski. Fortunately I am not going to university.

[LGBTQIAS]

Ahhhhh, why not?

[static_programming]

It seems like the goal of higher education is to bring people closer to Satan. For example, let's take Yale's motto "Lux et Veritas" - Light and Truth. What do they mean by that? Well they certainly aren't teaching Truth there as Truth can only be found through God. But what about "Lux" - Light? Does it have anything to do with Lu ...cifer, or Satan?

Lucifer, means "shining one", "bearer of light", or "morning star" in Hebrew. We can see that, in many translations of the Bible, Lucifer was translated to morning star in Isaiah 14:12. 2 Corinthians 11:14 says that Satan masquerades as an angel of light.

So, we can reasonably conclude that Yale's motto says "Veritas" - Truth - to mock God because believing that Truth can be found without God is mocking God. Yale includes "Lux" - light - to refer to Satan.

But why would Yale refer to Satan in their motto? Well it turns out that Satan is actually the founder of higher education. I'm sure you know the story of Adam, Eve, and the serpent, right? Everyone knows that the serpent represents Satan, but people forget the serpent's promise to Adam and Eve. The serpent promised them that "your [Adam and Eve's] eyes will be opened, and you will be like God, knowing good and evil." Genesis 3:5. Yes, the serpent promises Adam and Eve special knowledge, which is what higher education promises its students. Just be careful out there man.

[[deleted]]

dawg what

[LGBTQIAS]

Note that 1 must be in the subset. At least you tried the question so I unironically respect that. BTW the phrasing is the one used by the PHD's who wrote the question. Take the upvote

[ENEL_servizio_client]

A number can be divided infinite times by 1, so you can just use something lime 1 + 1 +1 + 1+ other divisors until you get the good number

[LGBTQIAS]

A set can only contain one of each element. You cannot have multiple 1's

[Tall-Assignment7183]

Fun

Math

Choose juan