Browse Groups

• I found some examples of: tau(n-1) = 16 tau(n) = 15 tau(n+1) = 14 where n+1 is not divisible by 5^6. Note that n+1 must be divisible by a prime to the sixth
Message 1 of 1 , Jan 28, 2002
View Source
I found some examples of:

tau(n-1) = 16
tau(n) = 15
tau(n+1) = 14

where n+1 is not divisible by 5^6.

Note that n+1 must be divisible by a prime to the sixth power (p^6),
but that -1 must be a quadratic residue modulo p^6.

This eliminates p = 2, 3, 7, or 11, so the smallest possible value
for p other than 5 is 13.

When p is 13, we have solutions for n:

859445130604^2
862953392956^2
903498588556^2
1008916097116^2
1158321143884^2
1461676435916^2
1734873825316^2
1755719985596^2
2740195949236^2
2858549305916^2
3544347983236^2

Note that when p = 13, each solution necessarily has:

n - 1 = p1 * p2 * 5 * 3
n = p3^2 * 2^4
n + 1 = p4 * 13^6

Of course, one may search for results with higher p with probable
success as well.
Your message has been successfully submitted and would be delivered to recipients shortly.
• Changes have not been saved
Press OK to abandon changes or Cancel to continue editing
• Your browser is not supported
Kindly note that Groups does not support 7.0 or earlier versions of Internet Explorer. We recommend upgrading to the latest Internet Explorer, Google Chrome, or Firefox. If you are using IE 9 or later, make sure you turn off Compatibility View.