Given a polynomial time algorithm to factorise an integer N, in unary representation, show that this does not imply that a polynomial time algorithm exists to factorise N in binary representation....

1. 
   

   
   Given a polynomial time algorithm to factorise an integer
   
   N,
   
   in unary representation, show that this
   
   does not
   
   
   imply
   
   that a polynomial time algorithm exists to factorise
   
   N in
   
   binary representation.
   

   
   

(Simply show that the length of

N



in a unary representation is expo­ nential in terms of its length in binary representation.)