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?

[QUOTE=enzocreti;537555]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?[/QUOTE]

Yes!!! 43^3*127^3+1 is.

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it is not multiple of 43




559 is multiple of 43 and congruent to 1 mod 31