Odd Perfect number must have the form r^{4n+1} p^2

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The discussion centers on the form of odd perfect numbers, specifically that they must take the structure r4n+1 p2. Alan seeks clarification on this proof, referencing Disckosn's "History of Number Theory" (vol 1, page 19) but finds it insufficiently detailed. CB suggests looking into Euler's proof for a more comprehensive understanding. This indicates a need for clearer resources on the topic of odd perfect numbers.

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Hi, I am looking for a textbook (or if you want you can explain it to me) that explains how we show that an odd perfect number if of the above form.

I checked it in Disckosn's History of number theory vol 1 page 19, but didn't quite grasped it (I believe he quite hand waved this proof).

Thanks in advance, Alan.
 
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Alan said:
Hi, I am looking for a textbook (or if you want you can explain it to me) that explains how we show that an odd perfect number if of the above form.

I checked it in Disckosn's History of number theory vol 1 page 19, but didn't quite grasped it (I believe he quite hand waved this proof).

Thanks in advance, Alan.

You can find an account of Euler's proof >>here<<

CB
 

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