Monday, September 13, 2010

Number Theory

This is from Number Theory. Might be trivial but its a good one.

Q- If n is not prime and euler function of n is a divisor of n-1 then prove that n has atleast three distinct prime factor ?

Try it.

2 comments:

  1. Well.. Here is the solution for this problem..

    We will use contradiction here..

    let n = ab where a and b are primes.

    Then euler function of n = n(a-1)(b-1)/ab

    Hence a congruency says..

    n-1 is congruent to 0 modulo euler function of n.

    that means..

    k (euler function of n) = n-1

    where k should be an integer..

    on opening.. we will see that k cannot be an integer.. hence Contradiction !!

    Hence Proved.

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  2. yea dis one was gud!...i had it last year from the book called HIGHER ALGEBRA by HALL N KNIGHT

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