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Why don't we consider non-units as quadratic residues? If we were more inclusive, too many theorems, proofs would have to say "quadratic residue relatively prime to $n$" instead of "quadratic residue." Also, for many years the focus was almost entirely on prime $n$. |
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10h
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About restriction of linear map You are welcome. That's what the site is for. |
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11h
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How to represent a sequence of odd numbers given specific criterea There is a substantial body of related results. There are various interpretations of your question. Here are some questions that will help any answerer. (i) Does order matter? Is $1,3,5$ different from $3,5,1$? (ii) Are we allowed things like $3,3,3$? |
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13h
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Is there a procedure to solve Diophantine Equations? @mixedmath: The general Fermat equation is an example of an exponential Diophantine equation. The Matiyasevich result is for ordinary Diophantine equations, no variables in the exponent. Undecidability of exponential diophantine equations was proved a number of years before Matiyasevich's result, by Davis-Putnam-Robinson. |
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13h
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Is there a procedure to solve Diophantine Equations? There is stuff in Logical Number Theory (Smorynski). Lots of other sources. It is essentially an application of the Hasse Principle. |
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What would be the expected number of targets which didn't get hit by any of the shooters? added 77 characters in body |
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What would be the expected number of targets which didn't get hit by any of the shooters? Distinguishable or not makes no difference here. |
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What would be the expected number of targets which didn't get hit by any of the shooters? There are quite a few important examples where a linearity argument gives the answer. For example, suppose we pick $k$ balls without replacement from a collection of $b$ blue and $r$ red. The indicator random variable approach used above quickly tells us the expected number of red. The combinatorial approach is a bit more messy. And I know of examples where the distribution is basically not accessible, but indicator rv works quickly. |
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What would be the expected number of targets which didn't get hit by any of the shooters? added 384 characters in body |
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answered | What would be the expected number of targets which didn't get hit by any of the shooters? |
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answered | Is there a procedure to solve Diophantine Equations? |
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About restriction of linear map added 402 characters in body |
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14h
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About restriction of linear map @mathscrazy: I had just added it. |
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14h
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answered | About restriction of linear map |
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Questions about $\mathrm{Aut}(\mathbb{Q} (\sqrt{2}, \sqrt{3})/\mathbb{Q})$ added 45 characters in body |
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Beginner Probability Question added 809 characters in body |
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answered | Beginner Probability Question |
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answered | Questions about $\mathrm{Aut}(\mathbb{Q} (\sqrt{2}, \sqrt{3})/\mathbb{Q})$ |
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Is game theory a part of math? Useful mathematics is still mathematics. |
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A quick Poisson distribution problem @DaleM: Thank you! I am not changing the remark at the end, since people reading the answer have access to your valuable reference. |
