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 Nov28 revised Trigonometry triangles expanded answer Nov28 answered Trigonometry triangles Nov28 comment Lower bound for logarithm? Since we were discussing bounds A "close to" 0, I assumed we were only interested in a bounding function for $x << 1$. Nov28 answered Continued fraction explanation Nov28 answered Lower bound for logarithm? Nov26 asked Can we determine which statements are incomplete due to Godel? Nov26 answered When proving a statement by induction, how do we know which case is the valid 'base'? Nov26 comment Prove that every practical number is either a power of two or a power of two times a non-trivial polygonal number @PeterTaylor I will do it if you wish. I want more experience updating OEIS. Let me know. p.s. love the domain name, and those laser swords. Nov24 awarded Quorum Nov24 answered Probability - rolling two dices and flipping one coin two times Nov24 comment Positively non-positive (from Brilliant.org) Whats wrong with my method? @YanYau, note that although a single case is not sufficient to prove that an N works, a single counter-example is sufficient to prove that a given N doesn't work, since you were asked to prove a condition always holds. Nov24 comment Derivative word problem - $s''(t) = a$, i.e the acceleration is constant and $(1) [s'(t)]^2 = 2as(t)$ Note that the prior question asks you to show why the solution is not in that form, so you shouldn't be surprised that there is no 'c' in the new form you are given. Nov24 comment Proving for every odd number $x$, $x^2$ is always congruent to $1$ or $9$ modulo $24$ I think you should make it its own answer, as this seems to be the real issue with the OP's understanding, not squaring and reducing numbers. Nov24 revised Proving for every odd number $x$, $x^2$ is always congruent to $1$ or $9$ modulo $24$ typos Nov24 comment Number of ways to arrange $5$ a and $5$ b letter As Andre says, how many places can the first 'a' go? The second? ... The fifth? But the 'a's are indistinguishable, so for each pattern we've produced, how many times did we create it by placing the 'a's in a different order? The end result will be what Adi wrote. Nov24 answered Differential Equations and Newtons method Nov24 answered Derivative word problem - $s''(t) = a$, i.e the acceleration is constant and $(1) [s'(t)]^2 = 2as(t)$ Nov24 comment Is $x^2$ always congruent to $(y-x)^2$ modulo $y$? How could you prove the cases where its true? that should be $-2xy$ in the expansion, luckily it doesn't change the conclusion. Nov24 answered Proving for every odd number $x$, $x^2$ is always congruent to $1$ or $9$ modulo $24$ Nov23 comment Prove that every practical number is either a power of two or a power of two times a non-trivial polygonal number @Jaycob, for the moment I was looking at lines of practical numbers for $x^2 \pm y$ or $P(x) \pm y$ (P being the pronic numbers), in a parallel to the patterns seen for primes in the Sacks number spiral. BTW, it was answering your other question that started me on the practical numbers and I haven't been able to give them up yet.