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Old 2021-08-08, 06:11   #4
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

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The two numbers which must be prime powers simultaneously are:

Code:
k mod 12      the forms for the two numbers
0      2^r*3^s+-1
1      2^r*3^s+1 and (2^r*3^s+2)/2
2      (3^r-1)/2 and 3^r-2
3      (3^r-1)/2 and (3^r+1)/4
4      2^r+1 and (2^r-1)/3 (only for k=16, since (2^r-1)/3 has algebra factors), or (3^r+1)/4 and 3^r+2
5      2*3^r-1 and A000265(2*3^r-2)
6      2*3^r+-1
7      2*3^r+1 and A000265(2*3^r+2)
8      2^r-1 and (2^r+1)/3
9      (3^r-1)/(2^s) and (3^r+1)/2 (only for k=81, since (3^r-1)/(2^s) has algebra factors)
10      (3^r+1)/2 and 3^r+2
11      2^r*3^s-1 and (2^r*3^s-2)/2

Last fiddled with by sweety439 on 2021-08-08 at 06:14
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