Eisentein theorem

[catcherintherye]

Main Question or Discussion Point

Then the proof goes on to consider coefficient of x viz a1=boc1 + b1co, and we know that a1=0modp and b1co=0modp so boc1=0modp.....


....2 questions why is b1co necessarily =0modp ? and secondly why does it follow that boc1=0modp? ....



.... i mean sure we know the sum b1co + boc1 =0modp but surely this doesn't imply b1co=0modp e.g 9=0mod3 but 9=5+4 and it is not true 5=0mod3

 

[catcherintherye]

btw does anyone know how to get all the mathematical symbols and stuff cos i'm getting really bored of typin g everything out long hand!

 

[jim mcnamara]

See the Latex discussion at the top of the PF forums:
https://www.physicsforums.com/showthread.php?t=8997

 

[cristo]

I don't know what you're trying to prove here, but the way you've worded it seems to suggest that you know that a1=0modp and b1co=0modp. Comparing this to your first equation, then clearly boc1=0modp.

However, I don't think this is what you're asking. Perhaps you should state the assumptions of the theorem!

 

[catcherintherye]

[ tex ] a^x_n [ /tex ]