Anonymous at Thu, 18 Jul 2024 13:52:08 UTC No. 16287186

3,4,2
6,4,1
8,3,1

Anonymous at Thu, 18 Jul 2024 13:56:51 UTC No. 16287194

we have the sum 8+64+256=328 so that gives 6 possibilities 8,64,256; 8, 256, 64; 64, 8, 256; 64, 256, 8; 256, 8, 64; 256, 64, 8
8^z can't be 256, and 4^y can't be 8
8, 256, 64; 64, 256, 8; 256, 64, 8
giving (3,4,2), (6, 4, 1) and (8, 3, 1)

Anonymous at Thu, 18 Jul 2024 14:11:15 UTC No. 16287214

>>16287186
>>16287194
You haven't proved that those are the only solutions. See you in algebra class.

Anonymous at Thu, 18 Jul 2024 14:14:42 UTC No. 16287224

>>16287214
sneed

Anonymous at Thu, 18 Jul 2024 14:16:58 UTC No. 16287228

>>16287224
?
No calculators in class. Confiscated. You can have it back tomorrow (today is Friday)

Anonymous at Thu, 18 Jul 2024 14:30:57 UTC No. 16287243

>>16287166
now do the same for rational numbers

Anonymous at Thu, 18 Jul 2024 14:36:26 UTC No. 16287253

>>16287166
I have understood the problem SIR! may I leave early from class today as well?

Anonymous at Thu, 18 Jul 2024 14:47:02 UTC No. 16287263

>>16287243
(8, 1.5, 2)

Anonymous at Thu, 18 Jul 2024 15:12:04 UTC No. 16287303

>>16287166
First you convert that problem into base two.

10^x + 10^(10*y) + 10^(11*z) = 101001000 = 10^(1000) + 10^(110) + 10^(11)

Now it's clear that z is either 1 or 10.
If z=10 then the 10^11 must come from 10^x so x=11 and y=100.
If z=1 then either x=1000 and y=11 or x=110 and y=100.

Converted into the decimal base the solutions are
(x,y,z) = (3,4,2)
(x,y,z) = (8,3,1)
(x,y,z) = (6,4,1)

You don't need a calculator for that.

Anonymous at Thu, 18 Jul 2024 15:13:51 UTC No. 16287307

>>16287186
>>16287194
I got the right answer too by listing out the powers of 2 and reasoning that only permutations of (256, 64, 8) are candidates and then eliminating the three permutations that don't work, but it feels kinda crude and brute-forcey as an approach. Is there a more elegant way?

Anonymous at Thu, 18 Jul 2024 15:23:01 UTC No. 16287318

>>16287166
i'd write a python script

Anonymous at Thu, 18 Jul 2024 15:29:31 UTC No. 16287325

>>16287318
this
t. masters student
I mean it's pretty easy to guess your ranges anyways, so it wouldn't take long at all

Anonymous at Thu, 18 Jul 2024 15:32:57 UTC No. 16287329

>>16287166
>computer science question
professor please go back

Anonymous at Thu, 18 Jul 2024 15:44:05 UTC No. 16287348

>>16287303
>Now it's clear that z is either 1 or 10.
That step is not justified at all.

Anonymous at Thu, 18 Jul 2024 17:55:43 UTC No. 16287504

>>16287224
What programming language is that? I never got into array based because of all the stupid ass symbols not on my keyboard. Is it obnoxious, or am I missing out?

Anonymous at Thu, 18 Jul 2024 17:57:40 UTC No. 16287509

>>16287318
>>16287325
>>16287224
What if it was
2^v + 4^w + 8^x + 16^y + 32^z = 68719544576
Or a bigger number. I'm sure there are fast algorithms for this, but who knows. Probably not in polynomial time

Anonymous at Thu, 18 Jul 2024 18:00:53 UTC No. 16287513

>>16287504
That's bqn. You set a mod key to type the symbols. It's not really worth it compared to python. It's like 10 seconds vs 1 minute

Anonymous at Thu, 18 Jul 2024 18:15:17 UTC No. 16287523

>>16287166
Maybe this guy should get a projector and a drawing screen that can translate his chicken scratch into legible text instead of this crap