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

Boring as in not challenging enough I hope you mean?

yes

that is correct

Have you heard of Euler's totient function?

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

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

the wolf says its a relatviely prime function
sounds similar to the \(\pi\)(n) to me

is 1 relativeley prime to 24?

Yes.

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

ah yes

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

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

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