# Mike

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 May30 comment Number of possible pairs from $\{1,\dots, n\}$ with $i < j$ My mistake, it is in fact simply ${n \choose 2}$ May30 asked Number of possible pairs from $\{1,\dots, n\}$ with $i < j$ May23 accepted How to find instances when $d(a,b) = p^2$ for $p$ a prime. May23 comment How to find instances when $d(a,b) = p^2$ for $p$ a prime. @MarkBennet it appears after looking at your answer and the original problem more closely that there are no such $(a,b) \in \Bbb N$ that satisfy this for $p$ a prime. Do you know how I might find the integral points on the surface $F(a,b,n) = 0 = d(a,b) - n$ for $n \in \Bbb N$? May23 comment How to find instances when $d(a,b) = p^2$ for $p$ a prime. @AmireBendjeddou $a, b \in \Bbb N$, sorry I should have mentioned these constraints. @ Mark Bennet: I'm sorry I think I may have misunderstood you. So your comment is that there are no pairs of the form $(1, b)$ satisfying the above equality? May23 asked How to find instances when $d(a,b) = p^2$ for $p$ a prime. May14 awarded Caucus May14 asked How to write down the maximal subgroups of $GL(9, \mathbb{C})$ May6 awarded Tumbleweed May3 accepted Galois relations between subfields May3 accepted Standard representation of $\frak S_4$ May3 accepted Weights versus roots Apr28 accepted How to compute the weights of $\Gamma_{3,1}$ the irrep of $\mathfrak{sl}_3\Bbb C$ Apr28 awarded Citizen Patrol Apr27 asked How to compute the weights of $\Gamma_{3,1}$ the irrep of $\mathfrak{sl}_3\Bbb C$ Apr27 comment Computing eigenvalues for $\mathrm{Sym}^2(\mathrm{Sym}^3 V))$ for $V = \Bbb C^2$ Thanks Jack, this works perfectly. I too noticed that the elements of $\mathfrak{sl}_2$ were acting like derivatives in terms of reduction of powers (it was clear that they would act via the typical derivation action on tensor products). I appreciate you taking the time to work this out for me in a very motivated manner. Apr27 accepted Computing eigenvalues for $\mathrm{Sym}^2(\mathrm{Sym}^3 V))$ for $V = \Bbb C^2$ Apr27 asked Weights versus roots Apr27 revised Computing eigenvalues for $\mathrm{Sym}^2(\mathrm{Sym}^3 V))$ for $V = \Bbb C^2$ edited tags Apr27 asked Computing eigenvalues for $\mathrm{Sym}^2(\mathrm{Sym}^3 V))$ for $V = \Bbb C^2$