Maths Problem

[Nagisa]

Show that for any positive integer n, there exists a positive multiple of n that contains only the digits 7 and 0.

[Planck's constant]

This one is too easy.


Look at the infinite sequence a1 = 7, a2 = 77, a3 = 777, a4 = 7777,. . . ak = 77........7  (k sevens)
Then look at the sequence of residues modulo n of its elements.
Since there are n residues modulo n, eventually two of them will coincide: ar = as (mod n), 0 < r < s.
Then as − ar will be a multiple of n containing only the digits 7 and 0 (in fact consisting of a string of 7’s followed by a string of 0’s.)


Give me a harder problem.

[Nagisa]

Give me a harder problem.

yo stop being such a tool. It seems you have copied from this website: http://www.math.northwestern.edu/~mlerma/problem_solving/putnam/quizzes/a5.pdf.

How about next time, i expect that you don't know what you're talking about and say that you should stop being ridiculous...

Edit: question 4, directly plagiarized their solution.

[Nagisa]

This one is too easy.


Look at the infinite sequence a1 = 7, a2 = 77, a3 = 777, a4 = 7777,. . . ak = 77........7  (k sevens)
Then look at the sequence of residues modulo n of its elements.
Since there are n residues modulo n, eventually two of them will coincide: ar = as (mod n), 0 < r < s.
Then as − ar will be a multiple of n containing only the digits 7 and 0 (in fact consisting of a string of 7’s followed by a string of 0’s.)


Give me a harder problem.

[Planck's constant]

It seems you have copied from this website: http://www.math.northwestern.edu/~mlerma/problem_solving/putnam/quizzes/a5.pdf.

Edit: question 4, directly plagiarized their solution.

Thats exactly what I did.

I copied the answer from the same website you copied the question

[Nagisa]

i put the question up to discuss with people and learn. dont ruin it for me dude

[Nagisa]

Thats exactly what I did.

I copied the answer from the same website you copied the question

you're mistaken,

[BubbleWrapMan]

is this real life?

[Nagisa]

is this real life?

or is this just fantasy?

[jadams]

must....resist....urge....to continue singCAUUUUUGHT IN A LAAAAAANDSLIDE

[Nagisa]

No escape from reality...

[FlorianK]

srly argonaut?!?
You give him a copied answer, because he copied the question?
Do you reckon everybody should only post questions that they made up themselves?
Only post up essays for topics that they didn't got from somewhere else, but thought of themselves?

I'll think of a different answer for that problem later today.

[Planck's constant]

srly argonaut?!?
You give him a copied answer, because he copied the question?
Do you reckon everybody should only post questions that they made up themselves?
Only post up essays for topics that they didn't got from somewhere else, but thought of themselves?

I'll think of a different answer for that problem later today.

No.
I posted the spoiler because this particular poster has a (brief) history of putting up so-called maths problems, making no attempt to participate in their solution, and using this whole thing as some kind of joke to taunt very good mathematicians on this site.

[kamil9876]

^ And what is so bad about that? Havn't there been many problems put up on this forum for the sake of amusement(e.g Fun Questions thread and TT's Math Thread)? I don't think that a mathematician is ever "taunted" by a problem but rather enjoys the challenge, unless they are insecure in which case they should just ignore it and let the others have fun. I reckon Nagisa just wants to share his interests with us and this is a good thing to promote, it can't hurt anyone.

edit: Ok, looking through Nagisa's profile, I can see some tension between the two and a big part of that is actually Nagisa's fault. I still do think that we shouldn't fuel it any further and try not to ruin any potentially good threads in the future.