help! It said the Fundamental Theorem of Arithmetic is used to prove. Let m = p1^e1 * p2^e2 ... ps^es, where pi is a prime. m|n if and only if pi^ei | n for all i.
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
all numbers can be written as a product of primes
primes have factors of 1 and themself
now this means that if m divide n
then every prime^exponent divides n
Not the answer you are looking for? Search for more explanations.
does it make sense?
maybe u need to say this statement too
ok, m | n means mk = n for some integer k
p1^e1 ( p2^e2 ... ps^es * k) = n implies p1^e1 | n
p2^e2 * (p1^e2 * p3^e3 ... ps^es k) = n implies p2^e2 | n
and so on to ps^es.
How do you prove the other direction?
what do u mean
it's an if and only if statement
okay since u saw that
p1^e1,p2^e2... all have to be factors
and u say primes cannot be decomposed into other primes so u are done
there is no other prime representation for m, so it goes both ways
well, we just proved that direction. The other direction is
if pi^ei | n for all i, then m|n
hmm to me its the same thing lol
ok how about saying it like this
if pi^ei | n for all i then
(p1^e1)(p2^e2)(p3^e3).....(pn^en) | n
because if* p1|n and p2|n then p1*p2|n if p1 and p2 are prime
this has to be true as a 2 different primes cannot share factors
so a lemma was used a long the way
Given p1 and p2 are primes. If p1| and p2|n, then p1*p2 | n
I think m * gcd(k1, k2, ... ks) = n will prove the result.