Arithmetic/Divisibility homework problem

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Homework Help Overview

The problem involves finding integer values of n that satisfy the divisibility condition n-2 | n²-n+3. Participants explore various methods to approach the problem, including the use of the quadratic formula and the definition of divisibility.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss using the Euclidean division and the quadratic formula to derive an equation involving a new variable k. There are questions about the necessity of finding the discriminant and how to interpret the results of the quadratic equation.

Discussion Status

The discussion is ongoing, with various methods being proposed and explored. Some participants express confusion about the algebraic steps, while others suggest alternative approaches. There is a recognition of multiple valid methods to solve the problem, but no consensus on the best approach has been reached.

Contextual Notes

Some participants note the importance of understanding the role of k in the problem and the implications of assuming integer values for n. There is also mention of the need to clarify assumptions about the nature of n (positive or negative integers).

  • #31


oay said:
Sorry for butting in, but I like to think of myself as a decent mathematician who has terrible difficulty with number theory.

I couldn't solve this at all. I had to write a program to solve for all cases for 1 to 1000 and I got the same answers: 3 & 7

Could someone please tell me where I'm going wrong analytically?

PS I've read post #2.

But you're missing -3 and 1 they are also answers in Z.
 
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  • #32


mtayab1994 said:
But you're missing -3 and 1 they are also answers in Z.
I got those too, I assumed n was positive, but I admit n=1 is a fair solution but is trivial.

How come Z comes suddenly into it?
 
Last edited:
  • #33


oay said:
I got those too, I assumed n was positive, but I admit n=1 is a fair solution.

Oh alright it's pretty easy solving it my way just look at my steps and see what I did. By the way that 5 I got in the numerator is the remainder you get when you do the Euclidean Division.
 
  • #34


mtayab1994 said:
Oh alright it's pretty easy solving it my way just look at my steps and see what I did.
I actually appreciated your method; I didn't say anything against it.
 
  • #35


oay said:
I actually appreciated your method; I didn't say anything against it.

What method do you use to solve them and by the way i have another one for you to solve if you want. Look at the other thread I'm going to post so you can see it.
 
  • #36


mtayab1994 said:
What method do you use to solve them and by the way i have another one for you to solve if you want. Look at the other thread I'm going to post so you can see it.
You've already replied to my post that said I couldn't solve it.
 
  • #37


oay said:
You've already replied to my post that said I couldn't solve it.

Oh sorry my fault.
 
  • #38


mtayab1994 said:
Oh sorry my fault.

No problem. Are you Indian?
 
  • #39


oay said:
No problem. Are you Indian?

Nope, I'm actually Moroccan. How about you?
 
  • #40


mtayab1994 said:
Nope, I'm actually Moroccan. How about you?
English
 
  • #41


Go take a look at my other thread so we can stop posting on this thread.
 
  • #42


mtayab1994 said:
Go take a look at my other thread so we can stop posting on this thread.
Which is where?
 

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