Wikipedia: Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm which, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns) can decide whether the equation has a solution with all unknowns taking integer values.
Wikipedia article: en.wikipedia.org
Solve this retards...
pic unrelated to Hilbert's problem
If the answer in OP pic is not 72 I'll kms
Ready the rope.
I think it's the sum of the numbers * 3
(1 + 5) * 3 = 18
(2 + 10) * 3 = 36
(3 + 15) * 3 = 54
(4 + 20) * 3 = 72
me too
I took the left side added up and subtracted it from the right. Then every subsequent number is previous number + 12 minus the numbers on the left added up.
So 18-6=12
36-12=24
54-18=36
72-24=48
72
72 because....
Left column of 18, 36, 54 goes 1, 3, 5 ... I guess the next should be 7.
Right column of 18, 36, 54 goes 8, 6, 4 ... I guess the next should be 2.
72.
Then I saw everyone else already got there using better maths, I just drew lines in my head.
I like
better than
because it is as if there is an invisible variable x = 3 on the left side that you are solving for.
Did you even fucking READ the wikipedia article. IT HAS BEEN PROVED NEGATIVELY. Utter fucking dumb mongrel, unironically kys.
sorry i am american who can do math
...
Modular arightmetic can solve some of it.
Suppose we want to examine:
x^2 + xy + z^2 + yz = 0
By Fermat's little theorem for primes p
a^p = a (mod p)
we have
x + xy + z + yz = 0 (mod 2)
x + z = -xy - yz (mod 2)
x + z = -y(x + z) (mod 2)
1 = -y (mod 2)
y = 1 (mod 2)
Another example:
w^3 + x^3 = y^3 + z^3
w + x = y + z (mod 3)
which is:
w + x = y + z + 3k
w + x - y - z - 3k = 0
And all possible solutions can be given straightforwardly.
that is fucked
But there is a way for every equation right? Even if there isn't a general algorithm?
Worst case scenario you just try to find solutions and realize there are none or there is at least one but every time you might have to do that differently (for different equations).
>Corresponding to any given consistent axiomatization of number theory, one can explicitly construct a Diophantine equation which has no solutions, but such that this fact cannot be proved within the given axiomatization.
Scientifically speaking, why does God hate us?
Took me less than 15 seconds to realize its x=3 for every equation. Answer is 72.
t. my first minute on Veeky Forums
Is this brainlet genius-wannabees board?
>took me less than 15 seconds
>15 seconds
user, I....
Trivial. We accept the first statement as a fact, then the rest follows by multiplication.
If 1+5=18 then 4+20 = 4(1+5) = 4(18) = 72.
False
False
False
24.