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May
21
revised How to understand the principles of the rule of three? By the way, who invented it?
edited title
May
19
comment How many ways there are to arrange a boolean $2\times5$ matrix such that there won't be two zeros one above the other
How many possibilities are there for the first row? Then, given some choice for the first row, how many possibilities are there for the second row? (This will depend on the number of zeros in the first row).
May
19
comment For which primes $p \ne 2,5$ does the congruence $x^2 \equiv 10 \mod p$ have a solution?
Yes, that is correct.
May
18
comment For which primes $p \ne 2,5$ does the congruence $x^2 \equiv 10 \mod p$ have a solution?
You only need to check the ones that arise from the two Legendre symbols being equal: $(1,1)$, $(1,4)$, $(7,1)$, $(7,4)$, $(3,2)$, $(3,3)$, $(5,2)$, $(5,3)$. Still a lot, but only half as many as you thought!
May
18
answered For which primes $p \ne 2,5$ does the congruence $x^2 \equiv 10 \mod p$ have a solution?
May
17
comment How to solve this two limits
Combine the terms to get $\frac{x-1}{x^2-1}$. Can you take it from there?
May
17
answered Ideals of the localization of a ring
May
16
answered Simplifying Radicals (Algebra II Basics)
May
16
answered How many possible strings exist given base string S and character C?
May
13
answered How to find this number, which is probably a very big prime or a product of big primes?
May
13
comment How to calculate these totient summation sums efficiently?
+1, Very nice, and quite efficient. How would you modify this algorithm if, for example, you only wanted the totient sum for odd numbers $\leq n$?
May
13
comment How to find this number, which is probably a very big prime or a product of big primes?
Except for four cases, all such $n$ less than three million have a difference equal to $169 = 13^2$; the other four have a difference of $221 = 13\cdot 17$.
May
11
answered System of equations involving sin and cos
May
9
comment Proving that these graphs are not isomorphic
Every vertex in $Y$ is part of a $5$-cycle; this is true of no vertex in $X$.
May
7
comment Let $p$ be a prime number $\ge2$ and $u = \cos\left(\frac 2p\pi\right)+i\sin\left(\frac2p\pi\right) \in \mathbb C$. Prove that …
Hint: try multiplying $f(x)$ by $x-1$ and see what you get.
May
7
comment Compute the determinant $D_n$
Computing this for $1\le n\le 10$, OEIS indicates that this might be A052585.
May
6
comment Out of 100%, if 52% of the population is type X, and 51% type Y…
Take a concrete example: suppose there are 100 people. Write down a Venn diagram if it helps you. How many of those 100 people have type X without type Y?
May
6
answered behavior of a rational prime in quadratic extension (definition)
May
6
answered Evaluate $ \lim_{x\to 0} \frac{\tan(4x)}{\sin(7x)}$
May
5
comment Calculating the Legendre symbols $\left(\frac{295}{401}\right)$ and $\left(\frac{713}{1009}\right)$ using quadratic reciprocity
Or even easier: $\big(\frac{12}{47}\big) = \big(\frac{3}{47}\big)\big(\frac{4}{47}\big) = \big(\frac{3}{47}\big)$.