Question

World's hardest math problem??!

Answer 1

o.o I bet no one can figure it out

Answer 2

What grade is this for?

Answer 3

Idk Some random problem

Answer 4

Seems like 11 or 10th?

Answer 5

No, I mean is this for 10th, 11th, or 12th grade?

Answer 6

This problem is hard even for undergraduate student.

Answer 7

ikr. lol

Answer 8

Where did you find this? @MasterprojectHD

Answer 9

On the world's hardest math problem. want me to to post the site?

Answer 10

@geerky42

Answer 11

Anyone want a hint?

Answer 12

"want me to to post the site?"

Sure.

Answer 13

http://www.businessinsider.com/if-you-can-solve-these-math-problems-you-are-as-smart-as-the-worlds-smartest-teenagers-2013-5

Answer 14

If the polynomial Pn(x) = (x6 + n) could be written as a product of 2 non-constant polynomials with integer coefficients, then by the Fundamental Theorem of Algebra one of those factors would represent a real root when Pn(x) = 0.

Let's plot Pn(x). First x6 is basically a parabola going thru (x,y) = (0,0) that opens upward and is symmetric about the y-axis. The + n is a positive or negative integer that raises or lowers the parabola along the y-axis leaving x alone.

Hence, for n>=+1, Pn(x) cannot have roots since it always has positive y, and so cannot be expresses in the product format.

For n=0, you get the degenerate case of x6 = 0 with 6 identical x=0 roots. so you can represent x6 = x1x5, x2x4 etc.

For n negative integers, the parabola gets lowered so there are exactly 2 distinct real integer roots:

If n = -1, the roots are x = +- 1 and a factorization is possible
If n = -64, the roots are x = +- 2 and a factorization is possible

If x = +-3, then n would be -729 = - (3)6, which exceeds your |n| < 500 constraint.

Answer 15

So P(-729)(+ -3)= -(3)6 Which exceeds your constraints. |n| ,< 500. CORRECT!

Answer 16

Nice copy-paste answer. @silenceforthedead

https://www.wyzant.com/resources/answers/59611/for_how_many_integers_n_with_ini_500_can_the_polynomial_pn_x_x6_n_be_written_as_a_product_of_two_non_constant_polynomials_with_integer_coefficients

Answer 17

^ I saw that too.

Answer 18

@geerky42

Answer 19

ye cx
i thought i put the link tho