mersenneforum.org sum of two positive cubes congruent to 1 mod Mersenne prime
 Register FAQ Search Today's Posts Mark Forums Read

 2020-02-14, 10:50 #1 enzocreti   Mar 2018 17×31 Posts sum of two positive cubes congruent to 1 mod Mersenne prime 344 and 559 are multiple of 43 and congruent to 1 mod a Mersenne prime 344 is infact congruent to 1 mod 7 (the greatest factor is 7) (344-1)=7*7*7 (the greatest factor is 7) 559 is congruent to 1 mod 31 (the greatest factor is 31) (558=...*31) 344 and 559 are sum of two positive cubes are there other number k that are multiple of 43, sum of two positive cubes and such that the greatest factor of (k-1) is a Mersenne prime? Last fiddled with by enzocreti on 2020-02-14 at 10:51
2020-02-14, 12:23   #2
sweety439

Nov 2016

53148 Posts

Quote:
 Originally Posted by enzocreti 344 and 559 are multiple of 43 and congruent to 1 mod a Mersenne prime 344 is infact congruent to 1 mod 7 (the greatest factor is 7) (344-1)=7*7*7 (the greatest factor is 7) 559 is congruent to 1 mod 31 (the greatest factor is 31) (558=...*31) 344 and 559 are sum of two positive cubes are there other number k that are multiple of 43, sum of two positive cubes and such that the greatest factor of (k-1) is a Mersenne prime?
Yes!!! 43^3*127^3+1 is.

 2020-02-14, 12:36 #3 enzocreti   Mar 2018 20F16 Posts .... it is not multiple of 43 559 is multiple of 43 and congruent to 1 mod 31

 Similar Threads Thread Thread Starter Forum Replies Last Post enzocreti enzocreti 2 2020-02-12 15:14 jux Miscellaneous Math 15 2015-08-30 06:21 mfgoode Puzzles 24 2007-08-06 16:20 fivemack Puzzles 4 2007-07-04 00:18 Numbers Puzzles 6 2005-09-03 00:26

All times are UTC. The time now is 20:38.

Mon Jan 18 20:38:55 UTC 2021 up 46 days, 16:50, 0 users, load averages: 2.58, 2.24, 1.97