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)/abHence a congruency says.. n-1 is congruent to 0 modulo euler function of n.that means..k (euler function of n) = n-1where k should be an integer..on opening.. we will see that k cannot be an integer.. hence Contradiction !!Hence Proved.
yea dis one was gud!...i had it last year from the book called HIGHER ALGEBRA by HALL N KNIGHT
Well.. Here is the solution for this problem..
ReplyDeleteWe 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.
yea dis one was gud!...i had it last year from the book called HIGHER ALGEBRA by HALL N KNIGHT
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