Tharsis

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bio website toolserver.org/~geohack/… location Stockholm, Sweden age member for 5 months seen 1 hour ago profile views 126

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 May16 awarded Enthusiast May11 comment Solving $(2x-1)\ln5=\ln2 + x\ln3$ for $x$This is a linear equation in $x$. Can you solve it for $x$ if you treat the logarithms as constants? If yes, then look up the logarithm laws to simplify the expression for $x$. May11 awarded Citizen Patrol May11 awarded Student May11 asked Natural extension of the divisor function $\sigma$ to the complex integers $\mathbb{Z}[i]$ May10 comment Last 2 numbers of the product of divisors@IvanLoh I have replaced the calculations with your observations, thank you! May10 revised Last 2 numbers of the product of divisorsadded Ivan Loh's improvement May9 comment Last 2 numbers of the product of divisorsIn the comment above, I used Euler's theorem and the binomial theorem. May9 reviewed No Action Needed Automata: 1=2, 2= 26, 3=1054, 4=5768, 5 =139314069504, 6 = ??? May9 reviewed No Action Needed Local Maxima in this function May9 revised How to derive $\cos\frac{n\pi}{3}=\frac{1+3(-1)^{[\frac{n+1}{3}]}}{4}$went further May9 comment Last 2 numbers of the product of divisors@darenn I used that $$21^{(53^3)}=21^{\displaystyle{\sum_{k=0}^3\binom{3}{k}40^k13^{3-k}}}\equiv_{10‌​0}21^{(13^3)}$$ and $$41^{61}=41^{\phi(100)+21}\equiv_{100}41^{21}.$$ May9 revised $X∈M_{m×1}(F)$ and $Y∈M_{1×n}(F)$: A Range Dimension Implicationimproved formatting and tags May9 suggested suggested edit on $X∈M_{m×1}(F)$ and $Y∈M_{1×n}(F)$: A Range Dimension Implication May9 revised What is $57^{46}$ divided by 17?improved formatting May9 suggested suggested edit on What is $57^{46}$ divided by 17? May9 awarded Custodian May9 reviewed No Action Needed What is $57^{46}$ divided by 17? May9 comment Last 2 numbers of the product of divisors@darenn Yes, I admit I used some help with the calculations. However, if necessary, all of this could be done with pen and paper, and some time. May9 comment Proving that every $2\times 2$ matrix $A$ with $A^2 = -I$ is similar to a given matrix@David It was an ansatz; it seemed like two degrees of freedom would suffice. Naturally, to simplify as much as possible, I first tried $$P=\pmatrix{0&A\\B&0},$$ but this implied that $A=B=0$. Seeing where it went wrong, I chose $$P=\pmatrix{1&A\\B&0}$$ instead.