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May
21
revised Subset sum problem is NP-complete?
added 2 characters in body
May
21
answered Subset sum problem is NP-complete?
May
21
revised What are a , b and c?
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May
21
answered Can a number have a prime factor that isn't a part of the number's prime factorization?
May
20
comment Another pigeonhole principle question
@Arvin: Yes, c(7,3) is correct. I was leaving that part for you to work out, but I see other respondents did the whole problem shortly after. Ah well.
May
20
awarded  Good Question
May
20
answered Another pigeonhole principle question
May
20
revised Preparation for Putnam?
edited tags
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
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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.