Pólya conjecture | Hacker News Reader

Pólya conjecture

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13 pointseru10 comments

While on topic of Polya, his book 'How to solve it' is considered a classic on the topic of problem solving http://en.wikipedia.org/wiki/How_to_Solve_It

"How I need a drink, alcoholic of course, after the heavy chapters involving quantum mechanics."

I've never heard this before, but I'll never forget it now. There are some more great Pólya quotes on his Wikipedia page: http://en.wikipedia.org/wiki/George_Pólya

"Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment."

Its probably the most expensive intellectual endeavor known to man (assuming you place a premium value on your time and life.)

A mere 906150257? I'm disappointed. Therefore:

Praptak's conjecture: every honest, non-tricky conjecture about natural numbers (that is false) has a counterexample not greater than 10^9.

So I guess Riemann's hypothesis must be true.

Reminds me of this problem:

Given a set of consecutive natural numbers, must one be coprime to all the others?

Did you mean s/must/can/ ? No?

Are you saying that the answer to the question is "No."? How is that true?

Consider the set: {3, 4, 5}. 3 is coprime to both 4 and 5. Am I misunderstanding the question?

But is that always be the case for all sequences?

No, my wording was what I meant. As the other reply points out, it is the usual case for a set of consecutive integers to have one member coprime to all the others. E.g.,

  {2,3} has 2 coprime to 3.
  {12,13,14,15} has 13 coprime to 12, 14, and 15.
  {24,25,26,27,28} has 25 coprime to 24, 26, 27, and 28.
  {48,49,50,51,52} has 49 coprime to 48, 50, 51, and 52.

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