Proving Perfect Number Equivalency with Mod 10

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Discussion Overview

The discussion revolves around proving that if \( n \) is an even perfect number, then \( n \equiv 6 \mod 10 \) or \( n \equiv 8 \mod 10 \). Participants explore the implications of the Euclid-Euler form of perfect numbers and engage in reasoning related to modular arithmetic.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant suggests that if \( n \) is an even perfect number, it must satisfy \( n \equiv 6 \mod 10 \) or \( n \equiv 8 \mod 10 \).
  • Another participant inquires about the Euclid-Euler form, indicating its relevance to the discussion.
  • A participant references the formula \( 2^{(p-1)} \cdot (2^p - 1) \) but expresses difficulty in obtaining the desired result with it.
  • Two participants claim to have proved the statement, sharing a link to an external site, though the validity of this proof is not established.
  • One participant notes the importance of the congruence of the exponential of 4 being either 4 or 6 mod 10, suggesting a possible oversight in their earlier reasoning.

Areas of Agreement / Disagreement

There is no consensus on the proof or the implications of the statements made. Multiple competing views and uncertainties remain regarding the proof of the modular conditions for even perfect numbers.

Contextual Notes

Participants have not fully resolved the mathematical steps or assumptions underlying their claims, particularly regarding the application of the Euclid-Euler form and the specific modular conditions.

nomather1471
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Show that ----> if n is even perfect number than n \equiv6(mod10) or n\equiv8(mod10)
 
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Do you know the Euclid-Euler form?
 
2^(p-1) *(2^p-1) formula i think you have said, i know this formula but i haven't get the result with this.
 
Last edited:
I can't believe to myself i think i proved :)
http://www.loadtr.com/465992-mmmmm.htm
 
Last edited by a moderator:
nomather1471 said:
I can't believe to myself i think i proved :)
http://www.loadtr.com/465992-mmmmm.htm

yea. it should be it
 
Last edited by a moderator:
it is important point of exponential of 4 is congruence 4 or 6 mod 10, i have missed it i think :)
 

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