(11 a)Show that if n is an odd perfect number, then n = pªm² where p is an oddprime and p = a = 1 (mod 4).b)Use part (a) to show that if n is an odd perfect number, thenn = 1 (mod 4).

Answered: Show that if n is an odd perfect numb…

Math

Advanced Math

Show that if n is an odd perfect numb prime and pa = 1 (mod 4). Use part (a) to show that if n n = 1 (mod 4).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

(11 a)
Show that if n is an odd perfect number, then n = pªm² where p is an odd
prime and p = a = 1 (mod 4).
b)
Use part (a) to show that if n is an odd perfect number, then
n = 1 (mod 4).

Expert Solution

Step 1

Here in the question, We have to show n is an odd perfect number then, $n = p^{α} m^{2}$ where, $p$ is an odd prime and $p \equiv a \equiv 1$ . To put it simply, a prime number can only be divided by itself and by one. Every prime number is an odd number, with the exception of number 2. The smallest odd prime number is three. No, not all odd numbers are prime numbers. We have to prove the result by Euler.

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