Friday, 12 July 2013

elementary number theory - Prove 2b1 does not divide 2a+1 for a,b>2




I'm trying to prove 2b1 does not divide 2a+1 for a,b>2. Can someone give a hint in the right direction for this?


Answer



Hint



Now, let a=qb+r with $0 \leq r

2a+1=2a2r+2r+1



Show that 2b1|2a2r and conclude that 2b1|2r+1. Now prove that this contradicts $0 \leq r

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