Divisors of a Number: n2+1 for 4k+1 Divisibility

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Homework Help Overview

The problem involves determining the divisibility of the total number of divisors of a number expressed in the form \( N = (7^{n1})(9^{n2})(11^{n1}) \) when \( n1 \) is even, specifically focusing on divisors of the form \( 4k+1 \).

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the factorization of the number and its implications for the divisors of the form \( 4k+1 \). There are attempts to clarify the role of \( n2 \) in the context of the problem, as well as the significance of using \( 9 \) instead of \( 3 \) in the factorization.

Discussion Status

Some participants are seeking assistance with the problem, indicating a lack of clarity on how to approach the divisibility aspect. Suggestions have been made regarding the factor decomposition and the nature of numbers of the form \( 4k+1 \), but no consensus or resolution has been reached.

Contextual Notes

There is a repeated emphasis on the condition that \( n1 \) is even, which may influence the interpretation of the divisor count. The use of \( 9 \) in the factorization raises questions about its properties in relation to \( 4k+1 \) forms.

jeedoubts
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1. Homework Statement
let N= (7^n1)(9^n2)(11^n1)
if n1 is even,then the total number of divisors of the form of 4k+1 must be divisible by?

correct answer is n2+1

3. The Attempt at a Solution
total number of divisors = (n1+1)(n2+1)(n1+1)
 
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jeedoubts said:
1. Homework Statement
let N= (7^n1)(9^n2)(11^n1)
if n1 is even,then the total number of divisors of the form of 4k+1 must be divisible by?

correct answer is n2+1

3. The Attempt at a Solution
total number of divisors = (n1+1)(n2+1)(n1+1)

can anybody please help me uot in this question?
 
jeedoubts said:
1. Homework Statement
let N= (7^n1)(9^n2)(11^n1)
if n1 is even,then the total number of divisors of the form of 4k+1 must be divisible by?

correct answer is n2+1

3. The Attempt at a Solution
total number of divisors = (n1+1)(n2+1)(n1+1)

can anybody please help me out in this question?
 
Hm... I don't have the solution, but can give some idea: The factor decomposition is funny, using 9 instead of 3. Anyway, put it like 9^n2 (7*11)^n1. Now get numbers of the form 4k+1: 1, 5, 9, 13, 17, 21, 25... 81... So, you see: powers of 9 are of the form 4k+1. You have to prove that no number of that form can be a multiple of 7 or 11.
 

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