Question

find all pairs of positive intergers (x,y) for

Answer 1

a)\[3^x=2^xy+1\]
b)\[x^y=y^{x-y}\]

Answer 2

3^x = 2^x y + 1
y =0, x=0 <-- this works ... since the lhs is power of 3

Answer 3

x=1, y=1 also works where you will get 3 = 3

Answer 4

so we just try out numbers

Answer 5

no ...we can't do that. diophantine equations have always been my weaknesses. I'm just fooling around.

Answer 6

if 3^n -1 is of form divisible by 2^n, then we have solutions of it.

Answer 7

actually i never knew that they are called that diophantine

Answer 8

\[3^x-2^xy=1\]
but we can try x=1,2,3,4
and see if they yield the y value to give 1

Answer 9

for these types of question, you should probably ask mukushla
till then let me fool around.

Answer 10

lol thanks a lot