Teenager Solves Stubborn Riddle About Prime Number Look-Alikes

Re:Teenager Solves Stubborn Riddle About Prime Number Look-A... by jablongo on Thursday October 13, 2022 @05:07PM (#33196496)

> A computer program to factor any polynomial equation string input to it: Do you mean a program to solve for f(x) = 0 using numerical approximation? Factorization has a specific meaning and is not necessarily possible for quintic and higher-degree polynomials / there is no closed form solution like the quadratic formula for n>=5.

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Re:Teenager Solves Stubborn Riddle About Prime Number Look-A... by THENATHE on Thursday October 13, 2022 @06:26PM (#33197282)

If they’re talking about the quadratic equation, this is likely 8th grade to 10th grade in the US education system. Factoring would be y^2 = 3(ab)^2 + c^2, get y all alone so it’s y = _____

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Re:Teenager Solves Stubborn Riddle About Prime Number Look-A... by casey2 on Thursday October 13, 2022 @08:20PM (#33198219)

Yes, polynomial factorization does have a specific meaning. You should learn it. https://en.wikipedia.org/wiki/Factorization_of_polynomials

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Re:Teenager Solves Stubborn Riddle About Prime Number Look-A... by civilized on Thursday October 13, 2022 @10:17PM (#33198891)

No, all real polynomials can be completely factorized (over the complex numbers). Whether the roots can be expressed in closed form is irrelevant.

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Re:Teenager Solves Stubborn Riddle About Prime Number Look-A... by ctchocula on Friday October 14, 2022 @05:21AM (#33201337)

To clarify, there do exist closed form solutions for quintic functions; they just cannot be expressed using rationals and a limited set of operations of additions, subtractions, multiplications, divisions, and root extractions. However, if you do not limit yourself to those operations, there do exist closed form solutions to quintics. See [1] for a few examples.

[1] https://mathworld.wolfram.com/QuinticEquation.html

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