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Old 2020-08-27, 07:50   #1
enzocreti
 
Mar 2018

17·31 Posts
Default ec exponents in position 9n

a(9)=36
a(18)=1323
a(27)=69660
a(36)=360787



pg(36), pg(1323) and pg(69660) and pg(360787) are primes




a(9) is the 9-th exponent leading to a ec prime


a(18) the 18-th


a(27) the 27-th


a(36) the 36-th




36,1323,69660 and 360787 are divisible by a perfect square




36 and 69660 (even) are divisible by a square which is a 3 smooth number (infact 36 is divisible by 36 which is 3 smooth, 69660 is divisible by 18^2 whcih is 3 smooth)


1323 and 360787 (odd) are divisible by 21^2 and by 7^2 which are squares that are 7-smooth numbers




so 36,1323,69660, 360787 are divisible either by 3^2*6^2 or by 3^2*7^2 or by 6^2 or by 7^2




360787 (mod (14^3)) is 1323


36 and 69660 even are of the form 8k+4


1323 and 360787 (odd) are of the form 8k+3

Last fiddled with by enzocreti on 2020-08-27 at 09:48
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