How can you find all b's <= 100 natural numbers such that there exists an a s.t. floor(100 * a/b) = 314?
#Find all b's <= 100 such that there exists an a natural number s.t. [100*a/b] = 314
cold hinge
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How can you find all b's <= 100 natural numbers such that there exists an a s.t....
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mystic vapor
How can you find all b's <= 100 natural numbers such that there exists an a s.t....
I need to see the original text of the problem.
cold hinge
That is the original problem
It was question number 1 on my number theory exam
And I had no idea on how to approach this problem
Let me repeat myself:
Find all "b" non-zero natural numbers <= 100 such that there exists an "a" natural number floor(100*a/b) = 314
mystic vapor
That is the original problem
It's not the original text, but I accept your explanation for why that's unavailable.
cold hinge
Am I misunderstanding but what do you mean by original text then?
Like a picture of my exam?
mystic vapor
Yes, exactly.
cold hinge
Anyway
Thanks for taking your time to think on this problem
A first observation is that for b = 1,2 4, 5, 10, 20 ,25 there does NOT exist an a
So these number are already out from the start
mystic vapor
Strictly speaking there's infinitely many b's.
mystic vapor
...what?
mystic vapor
b non-zero natural numbers <= 100
Look, having the problem written so poorly makes it hard to read, sorry.
That's one of many reasons why I prefer photos of original text.
I don't mean to be rude about it, but like, it's very important to state the problem clearly and exactly.
cold hinge
How many of the 1, 2, 3, ..., 100 there exist an a such that floor(100*a/b) = 314
mystic vapor
That's not even grammatically correct, but setting that aside
What does the floor function do?
mystic vapor
Therefore, if floor(100a/b) = 314, what can we say?
cold hinge
314 <= 100a/b < 315
mystic vapor
Therefore?
...therefore: 314b <= 100a < 315b 0 <= 100a - 314b < b
@cold hinge Recognize the middle term there?
cold hinge
Bezout?
mystic vapor
Right. And what's that?
mystic vapor
...you don't have to tell me that.
cold hinge
Too late
mystic vapor
It's not too late to apologize and yet you haven't.
cold hinge
Alright
Forgive me
I wasn't able to type when I had 2 use both hands with my diarheatic situation
With that out of the way
Lets focus on the problem again, shall we?
mystic vapor
Why did you tell me more?
cold hinge
Too late
mystic vapor
It's not too late for me to stop helping you.
mystic vapor
It's hard to believe you when that's not your first reaction.
mystic vapor
Yes, you go back to your problem, and I go somewhere else.
mystic vapor
Too late.
mystic vapor
How does Bezout work with the inequality?
Have fun figuring that out while I mourn my appetite.
cold hinge
Have fun figuring that out while I mourn my appetite.
Big doodoo response
mystic vapor
Big doodoo response
Do you think that belittling me is a good way to get me to help you?
mystic vapor
That's not how a dialect works.
mystic vapor
How in the hell could you possibly not realize that?
cold hinge
+close
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