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/sci/ - Science & Math

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3011194 No.3011194 [Reply] [Original]

my face when every rational number is the sum of three cubes.

>> No.3011209

why is this knowledge necessary

>> No.3011241

Is that an e-book on your pic OP? Where did you get that?

>> No.3011542
File: 34 KB, 400x268, laughing-girls-thumb9109825.jpg [View same] [iqdb] [saucenao] [google]
3011542

>>3011209

>> No.3011570

1 and 2

/thread

>> No.3011575

>>3011570
<div class="math"> 1 = 1^3 + 0^3 + 0^3 </div>

>> No.3011879

-26 ?

>> No.3011882

>>3011879
There are negative cubes, that won't get you anywhere.

>> No.3011887

4?

>> No.3011938

>>3011879
>>3011887

Well?

>> No.3011991

>>3011887
3^3+(-2)^3+1^3 = 9 -6+1 = 4
>>3011879
cant find this one

>> No.3011999

>>3011879
(-3)^3+1^3+0^3=-27+1+0

>> No.3012019

>>3011991
>>3011991

dude (-2)^3 = -8, not -6

>> No.3012029

3^3 =/= 9

>> No.3012039

Guys, it says three RATIONAL cubes. Not three INTEGER cubes.

>> No.3012063

>>3012039
Every integer is a rational number...

>> No.3012072

>>3012063
>>3012039

i think he's just saying that we can use rational numbers too, not just integers to solve these

>> No.3012080

>>3012072
This.
Everyone's been trying integer-only solutions.

At this point, I'd either accept existence of a general proof or write a script to brute-force solutions.

>> No.3012108

>>3012080
>i'd acept existence of a general proof
just have a look at OP's image then

>> No.3012119

>>3012108
lol
Yeah, that's what I meant.

>> No.3013325

>>3012063
integer is subset of rational

im more curious as to any restrictions on t, or specifically, t^3. I'd assume it is also rational, or the proof isn't of much use.

I guess you'd just need to prove that the sum of any 3 rational numbers cubed is rational

afternoon=salvaged :D

>> No.3013342

Rational numbers? Well then this is a pretty retarded theory then.

>> No.3013357

>>3013325
ok here's my shot at it:

a,b,c, rational numbers.
a,b,c can be expressed as fractions a=d/e,b=f/g,c=h/i, where, by definition, d,e,f,g,h,i are integers.

d^3/e^3 + f^3/g^3 + h^3/i^3 = r*t^3

we know that any integer cubed is an integer. We will use capitals to denote the cubed values:

D/E + F/G + H/I = r*t^3

we know that the sum of rational numbers is rational, so we will denote D/E + F/G + H/I as R

R = r*t^3
R/r = t^3

we already had the restriction that r is rational and we have shown that R is rational. since we have expressed t^3 as one rational number divided by another, we know that t^3 is rational.

QED

>> No.3013365

>Every even integer greater than 2 can be expressed as the sum of two primes.

http://en.wikipedia.org/wiki/Goldbach%27s_conjecture

>> No.3013387

>>3013365
4 = a^2 + b^2

a,b, primes

smallest prime number is 2, so a and b's minimum values are 2

4 = a^2 + b^2
4 = 2^2 + 2^2
4 /=8

we see that the smallest sum of a pair of primes is 8, which would exclude 2,4, and 6 from the set of even integers that could be expressed as the sum of two squared primes.

>> No.3013412

>>3013387
lol i read statement wrong

at least i proved it good D: