Add to ORKGInternational audienceBrent, Cohen, and te Riele proved in 1991 that an odd perfect number N is greater than 10^300. We modify their method to obtain N > 10^1500. We also obtain that N has at least 101 not necessarily distinct prime factors and that its largest component (i.e. divisor p^a with p prime) is greater than 10^62
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...
We say n ∈ ℕ is perfect if σ (n) = 2n, where σ(n) denotes the sum of the positive divisors of n. No ...
University of Technology, Sydney. Department of Mathematical Sciences.A long standing unanswered que...
International audienceBrent, Cohen, and te Riele proved in 1991 that an odd perfect number N is grea...
Abstract. Let σ(n) denote the sum of positive divisors of the natural number n. Such a number is sai...
If N is an odd perfect number with k distinct prime factors then we show that N < 2^(4k) . If some o...
Abstract. A 1913 theorem of Dickson asserts that for each fixed natural number k, there are only fin...
In this work we construct a lower bound for an odd perfect number in terms of the number of its dist...
AbstractIt is not known whether or not there exists an odd perfect number. We describe an algorithmi...
International audienceEllia recently proved that if N is an odd perfect number such that rad(N) > √N...
In this work we construct a lower bound for an odd perfect number in terms of the number of its dist...
International audienceEllia recently proved that if N is an odd perfect number such that rad(N) > √N...
A perfect number is defined as a number n for which the sum of the divisors of n equals 2n. All perf...
Abstract. Let σ(n) denote the sum of the positive divisors of n. We say that n is perfect if σ(n) =...
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...
We say n ∈ ℕ is perfect if σ (n) = 2n, where σ(n) denotes the sum of the positive divisors of n. No ...
University of Technology, Sydney. Department of Mathematical Sciences.A long standing unanswered que...
International audienceBrent, Cohen, and te Riele proved in 1991 that an odd perfect number N is grea...
Abstract. Let σ(n) denote the sum of positive divisors of the natural number n. Such a number is sai...
If N is an odd perfect number with k distinct prime factors then we show that N < 2^(4k) . If some o...
Abstract. A 1913 theorem of Dickson asserts that for each fixed natural number k, there are only fin...
In this work we construct a lower bound for an odd perfect number in terms of the number of its dist...
AbstractIt is not known whether or not there exists an odd perfect number. We describe an algorithmi...
International audienceEllia recently proved that if N is an odd perfect number such that rad(N) > √N...
In this work we construct a lower bound for an odd perfect number in terms of the number of its dist...
International audienceEllia recently proved that if N is an odd perfect number such that rad(N) > √N...
A perfect number is defined as a number n for which the sum of the divisors of n equals 2n. All perf...
Abstract. Let σ(n) denote the sum of the positive divisors of n. We say that n is perfect if σ(n) =...
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...
We say n ∈ ℕ is perfect if σ (n) = 2n, where σ(n) denotes the sum of the positive divisors of n. No ...
University of Technology, Sydney. Department of Mathematical Sciences.A long standing unanswered que...