Well?

ramen nougat? what?

Can i see your worksheet?

>Infinitely many solutions
not if you restrict yourself to natural numbers, which the question does

Thats not whats happening here since the quotients dont need to be natural numbers.

To the short bus with you

I thought diophantine equtions were like
ax+by=c

Its a=15.something
b=1 c=1

Whole values only

Alon amit showed how to solve a similar equation on quota quora.com/How-do-you-find-the-integer-solutions-to-frac-x-y z- -frac-y-z x- -frac-z-x y-4?encoded_access_token=6bbe8da22f3848c0a530c01b1122540c

wait, is a=b=c, or not?

If they were LHS gives 3/2

Lol

First thing to do is to realize that multiply a, b, and c by a constant multiple does not change the value of that sum. Next, if you just let a be a rational p/q, and set b=c=1, then solving for a like a quadratic will yield an irrational result. This implies that no two numbers can equal each other. Once you have this, do the substitution in the pic and get to the reduction I did, taking note that if a, b, and c are whole numbers, then so are x, y, and z. Once you get here, this fraction must reduce over x,y, and z in order to yield a while number. To divide by x, all terms with an x are divisible, leaving only yz^2+zy^2. Lastly, this term is divisible by both y and x, and from our co-prime rule and inequality, this term is indivisible by x. therefore the fraction cannot be reduced to a whole number, and therefore 16 is unobtainable using whole numbers. Fuck off with your Jewish tricks.

Nvm, I'm fucking retarded. That whole indivisibility thing is false. If x = 10, then (3)(15)^2+(15)(3)^2 is perfectly divisible by 10 and will yield 81.

Well that's a plot

Diophantine equations are just equations where you only care about integer solutions.

crazy how math do that except unironically

>positive hole values

what program is this?

c needs to be about 16 times larger than a+b
cheat a little and say a=0 is non-negative whole number

if b=1 c=15 we get 1/15 + 15/1 (missing 14/15ths)

a = 1 b = 1 c = 29 gives 2/30 + 29/2

how to pick values of a,b,c that give whole number results?

a+b = 8 b+c = 64 a = 2 b = 6 c = 58
a+c = 60
6/60 + 2/64 + 58/8

I think 16 is too high to get the remainders close to summing to a whole

Is this image implying that tomato is not a fruit?

What software is this? I fucking need it

Can you just take the derivative?

Grapher, a mac program

rather that opposing fruits and vegetables has little to do with biology

posts solution... gets ignored... Veeky Forums in a nutshell

Simple case of partial fraction decomposition.

Amazing. The best I could do was show that 15 < a/(b+c) < 16

Mixing science with history, chances are you are on mount stupid in more than one topic.

According to
ami.ektf.hu/uploads/papers/finalpdf/AMI_43_from29to41.pdf

the smallest solution has 414 digits.

>having no reading comprehension
The point is that "3 variables and 1 equation" alone does not necessarily lead to the conclusion that there's infinitely many solutions when you're dealing with natural numbers

I can report that there are no solutions if a, b, and c are each between 1 and 5000.

I determined that by exhaustive search.

The closest I got was:

a=124 b=139 c=4192 result = 16.00000004536067

If youre using a computer try up to one millioo

I have a more interesting result now. In searching a, b, and c each between 1 and 5000, none of the results is an integer.

The closest I got was:

a=37 b=4278 c=4781 result=1.999999999904425

So now I want to broaden the challenge: you are now allowed to put any positive integer on the right side of the equation.

>If youre using a computer try up to one millioo

That will be tough. It took 10 minutes for me to go up to 5000. The running time increases by the cube of the number, so going to 1 million would take about 8 million times longer.

How is integrating going to help you?

Yeah, that doesn't look too promising. There's a lot of different irrational factors all over the place in there. The chance of getting an integer for c seems pretty slim.

Damn that's so nice