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What is hyperspace in linear algebra?
In linear algebra text(Hoffman), it says "In a vector space of dimension $n$, a subspace of dimension $n-1$ is called hyperspace". The problem is the foll...
Apr 16, 2026
Archive: News
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Show that the equation $x^4 + 3 y^4 = 131$ has no integer solutions.
I have seen the result demonstrated by considering the equation$\pmod{5}$, but was wondering if this proof, working in $\mathbb{Z}_3$, is also valid, sinc...
Apr 16, 2026
![Find the greatest powers of $2$ dividing $10!$, $20!$, $30!$, $40!$ [duplicate]](https://news.conceivablytech.com/uploads/find-the-greatest-powers-of-2-dividing-10-20-30-40-duplicate_720.jpg)
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Find the greatest powers of $2$ dividing $10!$, $20!$, $30!$, $40!$ [duplicate]
I'm trying to find the greatest powers of $2$ dividing $10!$, $20!$, $30!$, $40!$, as part of a basic number systems course. I'm rather lost wit...
Apr 16, 2026
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List of not-especially famous problems in undergraduate level mathematics
I know lists of problems like these have been compiled before, but most tend to collect either extremely difficult problems ( like Collatz conjecture...
Apr 16, 2026
![Proving all primes are 1 or -1 modulo 6 [duplicate]](https://news.conceivablytech.com/uploads/proving-all-primes-are-1-or-1-modulo-6-duplicate_720.jpg)
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Proving all primes are 1 or -1 modulo 6 [duplicate]
Possible Duplicate: Is that true that all the prime numbers are of the form $6m \pm 1$? Q. Why is it that all primes greater than 3 are either 1 or -1 mod...
Apr 16, 2026
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How does atan(1) * 4 equal PI?
I needed the PI constant in C++, and I was lead to the answer that: const PI = atan(1) * 4 Note that despite involving code, I'm asking this from a m...
Apr 16, 2026
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Is standard deviation additive?
I am helping someone study for a statistics exam. I am quite good at most other math classes but it's been a while since I studied statistics. I am s...
Apr 16, 2026
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Proving Logical Equivalence with Laws of Logic
I'm working on Logical Equivalence problems and I'm having trouble understand what to do with this first problem. The problem is to show that th...
Apr 16, 2026
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Linear Algebra - Complete solution for Ax = b
Alright, I'm having some trouble understanding the "complete" solution for Ax = b. For instance, suppose $$A = \pmatrix{ 1 & 2 & 2 & 2 \\...
Apr 16, 2026
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What is the fastest way to find the characteristic polynomial of a matrix?
Finding the characteristic polynomial of a matrix of order $n$ is a tedious and boring task for $n > 2$. I know that: the coefficient of $\lambda^n$ is...
Apr 16, 2026
