timvermeulen
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 Dec15 awarded Caucus Dec15 comment Combinatorics in a Party. Exactly. I agree with @drhab and I think OP misunderstood the question. Nov19 comment Differentiability of a function on $\mathbb R$ such that $f(x+1)=f(x)$. I bet you meant "Finally, (c) is clearly false."? Nov5 revised Inequality proof by induction, what to do next in the step corrected spelling Nov5 comment Inequality proof by induction, what to do next in the step It's not extremely easy to see that $$2\left(\sqrt{n+2}-\sqrt{n+1}\right) = \frac{2}{\sqrt{n+2}+\sqrt{n+1}},$$ though. Nov5 answered Inequality proof by induction, what to do next in the step Sep30 awarded Explainer Jul2 awarded Curious Jun25 awarded Yearling Feb3 awarded Good Answer Nov20 revised Prove that $\sum_{1 \le t \le n, \ (t, n) = 1} t = \dfrac {n\phi(n)}{2}$ Removed \displaystyle in the title. Nov20 suggested approved edit on Prove that $\sum_{1 \le t \le n, \ (t, n) = 1} t = \dfrac {n\phi(n)}{2}$ Oct19 comment Let $T : V \rightarrow V$ be a linear operator. If $T^n = O_V$ for some $n \ge 1$, prove that $I_V + T$ is an isomorphism. Hint: use \left( and \right) for larger brackets when using exponents. Oct19 answered There are 10 different people at a party. How many ways are there to pair them off into a collection of five pairings? Sep22 comment How do I simplify $p^8-Q^8$? Though this is probably what's intended, I'm not sure if factoring symplifies it. Aug27 comment Extending primes Right, but then $73939133$ obviously is not the biggest prime you'll yield. Aug27 comment Extending primes I guess the prime you start with can only have one digit? Aug19 accepted Proving there are no integer solutions for $3x^2=9+y^3$ Aug19 comment Proving there are no integer solutions for $3x^2=9+y^3$ Thanks. I would never write a proof like my second one here on an actual contest or exam, but I've seen proofs to other problems that don't go into much detail at all (which I tried to mimic with my second proof). Aug15 comment How many ways can $2m$ be represented as the sum of 4 natural numbers $\le m$? Is this homework? Then please add the homework tag. Also, could you quote the original problem word for word? The question as it is now is a bit vague.