Question
In: Advanced Math
Following the Well Ordering Principle for Integers suppose n is an arbitrary integer greater than 1...
Following the Well Ordering Principle for Integers suppose n is an arbitrary integer greater than 1 and:
Z={x is a positive integer such that x is greater than or equal to 2 and x divides n}
Let y be the least element is set Z. Using proof by contradiction, show that y is prime.
Solutions
Expert Solution
Given 
be an integer greater than 1 .
That is the set 
is collection of all positive divisor of
which are greater than equals to 2 .
Now 
be the least element of
. So
is an element of
,
divides
.
There exist 
such that , 
.
Suppose
is not prime .
Then there exisy 
with 
such that 
.
divides
a contradiction to
be the least element of
and 
as
,
.
Hence
is a prime .
.
.
.
If you have doubt at any step please comment .
Colby Messinger answered 3 months agoRelated Solutions
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