peter and mathphile - 2019-06-11

« first day (48 days earlier) ← previous day next day → last day (56 days later) »

Mathphile

10:01 AM

for(n=1, 10^4, if(abs(floor(zeta(3-4n)))>=1, if(bigomega(abs(floor(zeta(3-4n))))==2, print(n))))

@Peter can you see what is wrong with this code?

Mathphile

10:37 AM

nvm found mistake

4 hours later…

Mathphile

2:08 PM

@Peter can you find integer solutions to $a^n + b^{n+1}= c^{n+2} $?

Peter

3:02 PM

? for(a=1,100,for(b=1,100,for(c=1,100,for(n=1,100,if(a^n+b^(n+1)==c^(n+2),print(
[a,b,c,n]))))))
[2, 5, 3, 1]
[4, 2, 2, 1]
[4, 11, 5, 1]
[7, 1, 2, 1]
[11, 4, 3, 1]
[11, 58, 15, 1]
[13, 70, 17, 1]
[15, 7, 4, 1]
[18, 3, 3, 1]
[19, 18, 7, 1]
[20, 14, 6, 1]
[23, 2, 3, 1]
[25, 10, 5, 1]
[26, 1, 3, 1]
[27, 18, 9, 2]
[28, 6, 4, 1]
[28, 8, 6, 2]
[28, 22, 8, 1]
[35, 36, 11, 1]
[39, 5, 4, 1]
[39, 31, 10, 1]
[40, 52, 14, 1]
[44, 9, 5, 1]
[45, 96, 21, 1]
[47, 13, 6, 1]
[47, 41, 12, 1]
[48, 4, 4, 1]
[53, 26, 9, 1]

Peter

3:52 PM

? for(a=1,1000,for(b=1,1000,for(c=1,1000,for(n=2,10,if(a^n+b^(n+1)==c^(n+2),prin
t([a,b,c,n]))))))
[27, 18, 9, 2]
[28, 8, 6, 2]
[63, 36, 15, 2]
[256, 64, 32, 3]
[433, 143, 42, 2]

Peter

4:20 PM

@Mathphile In conjecture 12) , $n^n-n$ is not semiprime for n = 3

Mathphile

4:37 PM

yes that was a mistake

can you find a solution for n=4 for $a^n + b^{n+1}= c^{n+2} $

Peter

4:51 PM

For $n=4$ , no solution with $1\le a,b \le 10^4$ exists

Mathphile

interesting