39 reputation
116
bio website oeis.org/wiki/…
location
age
visits member for 2 years, 10 months
seen Aug 14 '14 at 9:39

Three hard to prove conjectures from Alexander R. Povolotsky

1) n! + prime(n) != m^k (so far proven only for the case when k=2)

2) n! + n^2 != m^2 (so far proven only for the case when n is prime number)

3) n! + Sum(j^2, j=1, j=n) != m^2 (so far no proof)

where != means "not equal" and k,m,n are integers


7901234568 / 9876543210 * 1234567890 = 0987654312


24/Pi = sum((30*k+7)binom(2k,k)^2(Hypergeometric2F1[1/2 - k/2, -k/2, 1, 64])/(-256)^k, k=0...infinity)

Another version of this identity is: Sum[(30*k+7)Binomial[2k,k]^2(Sum[Binomial[k-m,m]*Binomial[k,m]*16^m,{m,0,k/2}])/(-256)^k,{k,0,infinity}]


10 Sep 23 '14
10 Jul 28 '14
0 Jul 26 '14
There were no net reputation changes on this day
10 Jul 24 '14
-90 Jul 20 '14
5 Jul 17 '14
5 Jul 16 '14
5 Jul 15 '14
2 Jul 13 '14
15 Jul 12 '14
-15 Jul 10 '14
10 Jul 9 '14
2 Jul 8 '14
5 Jul 7 '14
-45 Jul 6 '14
-2 Jul 5 '14
5 Jul 4 '14
10 Oct 31 '13
5 Sep 21 '13
5 Apr 5 '13
10 Feb 15 '13
10 Feb 7 '13
5 Jan 17 '13
-5 Nov 9 '12
-2 Sep 26 '12
2 Sep 14 '12
3 Sep 10 '12
10 Sep 8 '12
10 Jul 5 '12
-2 Jun 26 '12