Add to ORKGIt has been known since the time of Euler that an odd perfect number N (if it exists) must have the form N = paQ2 where p is prime and p = a = 1 mod 4 (see, e.g., [1, pp. 3–33]). Further, it has been shown that N must equal 1 mod 12, or 9 mod 36 [3], [2]. However, we can do a little better than this
Euler's structure theorem for any odd perfect number is extended to odd multiperfect numbers of abun...
A natural number $n$ is called {\it multiperfect} or {\it$k$-perfect} for integer $k\ge2$ if $\sigma...
The finiteness of the number of solutions to the rationality condition for the existence of odd perf...
An odd perfect number N is a number whose sum of divisors is equal to 2N. Euler proved that if an od...
AbstractLet n = παM2 be an odd perfect number; πα, with π prime, (π, M) = 1 and π ≡ α ≡ 1 (mod 4), i...
Let n=παΠkuk2bk be an odd perfect number; πα, with πэαэ1, (mod 4), is the Euler's factor. It is show...
AbstractLet n = παM2 be an odd perfect number; πα, with π prime, (π, M) = 1 and π ≡ α ≡ 1 (mod 4), i...
As shown by Euler an odd perfect number n must be of the form n=p^α m^2 where p≡α≡1 (mod 4) and p is...
As shown by Euler an odd perfect number n must be of the form n=p^α m^2 where p≡α≡1 (mod 4) and p is...
Let n=παΠkuk2bk be an odd perfect number; πα, with πэαэ1, (mod 4), is the Euler's factor. It is show...
A slightly alternative proof is presented which establishes a classic result of Euler on odd perfect...
AbstractStarting with Euler's theorem that any odd perfect number n has the form n = pepi2ei … pk2ek...
This article proves that a certain form of odd numbers cannot be perfect, it also provides an altern...
This article proves that a certain form of odd numbers cannot be perfect, it also provides an altern...
Euler's structure theorem for any odd perfect number is extended to odd multiperfect numbers of abun...
Euler's structure theorem for any odd perfect number is extended to odd multiperfect numbers of abun...
A natural number $n$ is called {\it multiperfect} or {\it$k$-perfect} for integer $k\ge2$ if $\sigma...
The finiteness of the number of solutions to the rationality condition for the existence of odd perf...
An odd perfect number N is a number whose sum of divisors is equal to 2N. Euler proved that if an od...
AbstractLet n = παM2 be an odd perfect number; πα, with π prime, (π, M) = 1 and π ≡ α ≡ 1 (mod 4), i...
Let n=παΠkuk2bk be an odd perfect number; πα, with πэαэ1, (mod 4), is the Euler's factor. It is show...
AbstractLet n = παM2 be an odd perfect number; πα, with π prime, (π, M) = 1 and π ≡ α ≡ 1 (mod 4), i...
As shown by Euler an odd perfect number n must be of the form n=p^α m^2 where p≡α≡1 (mod 4) and p is...
As shown by Euler an odd perfect number n must be of the form n=p^α m^2 where p≡α≡1 (mod 4) and p is...
Let n=παΠkuk2bk be an odd perfect number; πα, with πэαэ1, (mod 4), is the Euler's factor. It is show...
A slightly alternative proof is presented which establishes a classic result of Euler on odd perfect...
AbstractStarting with Euler's theorem that any odd perfect number n has the form n = pepi2ei … pk2ek...
This article proves that a certain form of odd numbers cannot be perfect, it also provides an altern...
This article proves that a certain form of odd numbers cannot be perfect, it also provides an altern...
Euler's structure theorem for any odd perfect number is extended to odd multiperfect numbers of abun...
Euler's structure theorem for any odd perfect number is extended to odd multiperfect numbers of abun...
A natural number $n$ is called {\it multiperfect} or {\it$k$-perfect} for integer $k\ge2$ if $\sigma...
The finiteness of the number of solutions to the rationality condition for the existence of odd perf...