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[QUOTE=rudy235;583019]I never quite understand what you are trying to say. Can you explain to the unwashed masses the function [B]pg[/B]? What is it? Paying guest? Picogram?[/QUOTE]

the last you said

215*107*12^2 is congruent to -71*6^6 which is congruent to 72 mod (331*139)


331*139*8 is congruent to -8 mod (215*107)


s^2 is congruent to 1 mod 23005

the first not trivial solution is

s=429

the second is s=9201

the third is s=13374

(13374^2-1)/23005 is congruent to -1 mod 6^5


215*107*(2+331*139*8)-1 is a multiple of 331*139 and 429^2


mod 429^2 we have

23005*184033-1 which is a multiple of 429^2 and 71


((184033*23005-1)/71-429^2)/429^2=18^2-1



92020 is congruent to 4*(2+331*139*8)^(-1) mod 429^2 and mod (331*139) so


92020 is congruent to 4*(368074)^(-1) mod 429^2 and mod (331*139)

the inverse of 368074 so is 23005

92020 is congruent to 4*(429^2-2^2)^(-1) mod (331*139*429^2)


maybe it is useful


431=(427)^(-1) mod 46009???




331259 for example is congruent to -(9203*4+1) mod (331*139)


and 331259 is congruent to 9203 mod 23004




(92020)^(-1)=23005 mod (331*139)




92020*23005=(46010)^2




92021 divides 215*107*(2+331*139*4)-1


pg(69660), pg(19179) are primes

maybe something useful can be derived from this:

69660 is congruent to 19179 which is congruent to 429^2 which is congruent to 9 mod (71)

69660 and 19179 are of the form 648+213s

probably there are infinitely many pg(648+213s) which are primes


in particular

6^6 is congruent to 19179 which is congruent to 429^2 which is congruent to 861 mod (71*43)

6^6 is congruent to 860 mod (214^2)


92020 is congruent to -2^0 mod (17*5413)

92020 is congruent to -2^1 mod (3*313*7)

92020 is congruent to -2^2 mod 11503

23005*(2+331*139*2^0)-1 is a multiple of 11503
23005*(2+331*139*2^1)-1 is a multiple of 3*313*7
23005*(2+331*139*2^2)-1 is a multiple of 17*5413