Arithmetic/Divisibility homework problem

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SUMMARY

The forum discussion revolves around solving the equation n-2 | n²-n+3 using Euclidean division and the quadratic formula. Participants emphasize the importance of correctly applying the quadratic formula, particularly in determining the discriminant. The final solutions for n, derived from the divisibility condition, are -3, 1, 3, and 7. The discussion highlights multiple methods for solving the problem, with a focus on understanding the underlying algebraic principles.

PREREQUISITES
  • Understanding of divisibility and the notation n-2 | n²-n+3
  • Familiarity with Euclidean division
  • Knowledge of quadratic equations and the quadratic formula
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the properties of divisibility in number theory
  • Learn about the quadratic formula and its applications
  • Explore different methods for solving polynomial equations
  • Practice problems involving Euclidean division and quadratic equations
USEFUL FOR

Students studying algebra, particularly those focusing on number theory and quadratic equations, as well as educators looking for problem-solving techniques in mathematics.

  • #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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