question

[obsidian crown]

Help me solve this algebra

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[zealous harness]

try graphing out the functions perhaps

but change the y to an x

and see how many interesectipns they have

then check if they’re integers

nvm that doesnt work

as they can be any value along the x axis

[final cloud]

$y = 3n : y^3+1 = 27n^3+1 \not = 3^x$ this does not work $y=1+3n : y^3+1 = 1+3 \cdot (...)+1 \not = 3^x$ same here $y=-1+3n : y^3+1 = -1+3 \cdot (...) +1 = 3 \cdot (...)$ so it can only work if $y = 2, 5, 8, ...$

[stable nova]

Ludwig

[zealous harness]

y=5
126-125=1
126=21*6 and not a power of 3?

513 (8^3+1)is also 9*51 and not a power of 3

unless you want OP to figure out which of those is actually real?

[final cloud]

I said that it can work, not that it does work

[zealous harness]

ah ok

you can also figure out y must be even or else y^3+1 is even and not 3^x

this still narrows it down to infinity

sadly

[final cloud]

so y can only be $y=2+6n$

[stable nova]

Ludwig

[granite gulch]

use catalan's conjecture