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 May 20 comment Logic Puzzle of the age of three sons If the answer were 1,6,6 and the two 6-yr-olds were born 11 months apart, wouldn't there still be an "oldest"? May 19 answered If $a|b$ and $c|d$, then $ac|bd$ 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?