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Old 2020-02-14, 10:50   #1
enzocreti
 
Mar 2018

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Default 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
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Old 2020-02-14, 12:23   #2
sweety439
 
Nov 2016

22×3×5×47 Posts
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Quote:
Originally Posted by enzocreti View Post
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.
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Old 2020-02-14, 12:36   #3
enzocreti
 
Mar 2018

17·31 Posts
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it is not multiple of 43




559 is multiple of 43 and congruent to 1 mod 31
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