Recent content by kmeado07

i don't know, I am confused!

you would start at n! + 1,000,003 ?

So there are n-2 consecutive non-primes starting with n! ?

ok, so a factor of n!+3 is 3, and a factor of n!+2 is 2 and so on. So a factor of n!+n is n. This shows that none of them is prime. How would i go about doing the second part of the question?

Is (n factorial + 2) a factor of it? Which would then apply to the others, which would show that none of them were prime. For them each to be prime, their only factors would have to be themselves and 1.

Homework Statement Let n be a part of the natural numbers, with n>=2. Consider the numbers [n factorial +2 ], [n factorial + 3], ..., [n factorial + n]. Prove that none of them is prime, and deduce that there are arbitrarily long finite stretches of consecutive non-prime nummbers in the...

This is ok if p doesn't divide n, but the question asks me for all integers n. So how do i show it's also true for when p divides n?

sorry, silly mistake. dividing by n would give me, n^(p-1) equivalent to 1 (mod p) which is fermat's little theorem. so is this all i need to do?

ok, so in my question, c=n ? So by dividing by n i would get, 1^p is equiavlent to 1 (mod p) How do i reach n^(p-1) on the left hand side?

Homework Statement From fermat's little theorem deduce that when p is prime, n^p is equivalent to n (mod p) for all integers n. Homework Equations The Attempt at a Solution I know from Fermat's Little Theorem that , n^(p-1) is equivalent to 1 (mod p), but i don't...

yea, thank you!

Homework Statement Find the limit of f(x)=[xcosx]/[x^3 + 1] as x tends to infinity. Homework Equations The Attempt at a Solution Can i use l'hopitals rule here? Or if not, what are the conditions for f(x) to meet so that i may use l'hopitals rule? Without using l'hop i know...

Homework Statement Show that the following series converges: Homework Equations Sum of (from n=1 to infinity) of [3^n + 4^n] / [3^n + 5^n] The Attempt at a Solution Some help on this question would be much appreciated as i really don't know how to start it. Thanks

Homework Statement Evaluate the following intergral: Homework Equations Intergral from gamma of (y)dz, where gamma is the union of the line segments joining 0 to i and then i to i+2 The Attempt at a Solution I have no idea how to do this!

Homework Statement For the following set, state and justify whether or not it is open or closed. Homework Equations A={z| I am z >1} The Attempt at a Solution I know the definition of an open set, but I am not sure how to use it to solve this question.