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May
19
answered How to “invent” a function?
May
18
comment Intuitive understanding of why the sum of nth roots of unity is $0$
@Pete L. Clark: I had a junior high school teacher who would write on a test "What is $\cos(90)$" and mark it wrong if you wrote 0. I'm not sure he inspired many students to become mathematicians, but to each his own I suppose. Here is how Wolfram Alpha responds: wolframalpha.com/input/?i=2cos%2872%29%2B2cos%28144%29
May
18
comment Intuitive understanding of why the sum of nth roots of unity is $0$
@Pete L. Clark: I'm not sure I follow. You are interpreting 72 and 144 as radians? From the context of the question it's clear he means degrees, in which case $2\cos(72)+2\cos(144)$ is $-1$ as stated.
May
16
revised A good book for learning mathematical trickery
edited tags
May
15
comment Concerning: presentations of rational numbers into sums
@quanta: Exactly. Which is why it's unlikely you can form a negative rational number via a sum of fractions with 1 over a natural number.
May
15
comment Concerning: presentations of rational numbers into sums
You might want to say positive rational numbers since negative rationals obviously cannot be formed with numerator 1 and natural-number denominators. (The Putnam problem cited by Chandru1 specifies that the numbers be positive.)
May
14
awarded  Nice Answer
May
14
revised Intuitive understanding of why the sum of nth roots of unity is $0$
Expanded answer for n > 3
May
14
revised Intuitive understanding of why the sum of nth roots of unity is $0$
Changed 74 -> 72 everywhere
May
14
comment Intuitive understanding of why the sum of nth roots of unity is $0$
@Jason: No, you won't get 1. For $x_1+x_4$ you'll get something like $.62$. But for $x_2+x_3$ you'll get about $-1.62$ which gives the $-1$ needed to cancel out the $1$ and obtain 0. Unfortunately, except for the $n=3$ example I gave, you don't get unit vectors along the way. I'll expand my answer for odd $n > 3$ later when I get time.
May
14
suggested approved edit on Intuitive understanding of why the sum of nth roots of unity is $0$
May
13
answered Intuitive understanding of why the sum of nth roots of unity is $0$
May
12
comment Help to understand material implication
@joriki: Thanks, I modified my answer (slightly) to perhaps help in this respect.
May
12
revised Help to understand material implication
Minor clarification
May
12
answered Help to understand material implication
May
12
comment Edge of factoring technology?
@noonand: No problem, I appreciate the comment. :)
May
11
comment Edge of factoring technology?
Blah, sorry. I had "Schorr" originally (probably confused with Claus Schnorr, another cryptographer) and I "fixed" the spelling from "Schorr" to "Schor". Thanks to J.M.
May
11
answered Edge of factoring technology?
May
10
answered Find a number $b$ such that $a\cdot b\equiv 1\mod m$
May
9
answered Your favourite maths puzzles