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October 5th, 2010, 06:51 AM  #1 
Newbie Joined: Mar 2010 Posts: 23 Thanks: 0  Problems driving me crazy.(Primes,Fermat,Euler)
1) Show that if a is an integer and mdc(a,9)=1, so a^7 congruent a (mod 63). Comments: ?(7) = 6 e ?(9) = 6 helps in any way? 2)Show that if n is a pseudoprime for the base a but not a pseudoprime for the base b, so n is not a pseudoprime for the base ab. Comments: Should I use a^b1 congruent 1 (mod n) or a^n congruent a (mod n) ? 3) Prove that if ?(n) is prime, then n=3,4 or 6. Comments: Computing ?(3), ?(4) e ?(6) gives us prime numbers, but how to give a normal proof? 
October 5th, 2010, 10:30 AM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Problems driving me crazy.(Primes,Fermat,Euler) Quote:
Generally, you'll want to work mod 7 and mod 9 then crt the results together. Quote:
Quote:
 

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