Question

So, number theory homework consists of questions like:

1) is 107 a prime number?
2) make a sieve to find all primes less than 200
3) what is the smallest prime of the form (5n+4)
4) is 1716 divisible by 22
5) what are the factors of 12

Welcome to college math .... :/

Answer 1

What one do you need help with? Sieve of Erastosthenes should be enough for the first 2.

Answer 2

i need help with the sheer boredom of it all :) ive already finished them, i just found them to be soooo boring.

Answer 3

Boring as in not challenging enough I hope you mean?

Answer 4

yes

Answer 5

I'm guessing you've just started this at college, in which case the lecturers will have to cover the basics to get everyone to the same level before they proceed with the more advanced stuff.

Answer 6

that is correct

Answer 7

Have you heard of Euler's totient function?

Answer 8

ive heard of euler, cant say i know what a totient is tho

Answer 9

Ok, you will no doubt learn about it this year so you might find it interesting to read about.

Answer 10

the wolf says its a relatviely prime function

sounds similar to the \(\pi\)(n) to me

Answer 11

is 1 relativeley prime to 24?

Answer 12

Yes.

Answer 13

If integers n and k are relatively prime then gcd(n, k)=1 is the technical definition.

Answer 14

ah yes

Answer 15

i asked the teacher if when doing proofs on teh test, if we can make a not on the side margin saying that its fairly simple enough but that there is not enough room :)

Answer 16

I don't think the Fermat argument will suffice in an exam unfortunately :P

Answer 17

i think a classmate of mine did a paper in which he mentioned the totient function, if i recall correctly it has a relationship with a fibonnacci sequnce

Answer 18

I'm not sure how it could have a relationship with the fibonacci sequence, I'd be interested to see if it did though.

Answer 19

ill see him later today, if hes in class, and ask him to refresh me memory :)

Answer 20

I have some very interesting problems we received as assignments in my first year number theory course, I could have a look for them if you are interested?

Answer 21

1.107 is an prime number 5. factors of 12; 1,2,3,4,6, and 12