#Number theory (Division Algorythm)

14 messages · Page 1 of 1 (latest)

vital saddle
#

This question has been answered differently by me than the book although I have the feeling that my solution is good as well, I am not a professor so I can't be sure. The picture is my solution and the one on the left is the book's solution (with the question given above it). Can anyone tell me why my answer would be wrong?

PS: the n(n+1)/2 identity has been proven (by induction) in a previous exercise in the book which is why I wrote it down there at the end.

Thanks for reading

vraagje_getal_theorie.png
rich crownBOT
#
  1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
  2. Wait patiently for a helper to come along.
  3. Once someone helps you, say thank you and close the thread with:
    +close
  4. Feel free to nominate the person for helper of the week in #helper-nominations
  5. Do not ping the mods, unless someone is breaking the rules.
  6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:
midnight heath
#

or latex

#

this is very hard to read, I'm sure people will misread something

vital saddle
#

The difference basically lies here: I substitute an odd number once while they substitute another time with 2n & 2n+1

#

They are more general but why is only 1 substitution not enough

tribal coral
#

@vital saddle
I think you have a mistake between line 2 and 3
In line 3 the 4th and 5th terms should be 16n^3 + 16n^2

Regarding the n(n+1)/2 thing, it is correct. You don't actually need the formula since you can just say that one of n and (n+1) is even and therefore n(n+1)/2 is an integer

After the 3rd line I don't understand much so I am going to assume you did some algebra wrong later as well

vital saddle
#

yep, these terms are different. And with the correct terms I end up with something which needs a second substitution 2 proof it which would be the one the book suggests. Thanks for finding the mistake, I'll be more aware in the future.

#

You'd end up with showing 40n^2 + 24n is in the form of 16k . Substituting 2n or 2n+1 for n shows it does

vital saddle
icy canyonBOT
#

@vital saddle has given 1 rep to @tribal coral

vital saddle
#

+close