Diophantine Equation with no solutions

[e2m2a]

Does anyone know if this Diophantine equation is impossible to solve for all values of s?

C^u = A^u + B^s, where u = 2s

For example, is there no integer solution for C,A, and B for the following:

C^22 = A^22 + B^11

 

[BvU]

It is possible to solve $C^2 = A^2 + B$ with integers for s = 1

 

[e2m2a]

But what about for s > 1? Are there no solutions and if so, is there a proof for this?

 

[BvU]

Are the restrictions going to come in one at a time or is there a complete problem description ?
'Integers' is quite a bit more than 'natural numbers > 2' $\qquad$ [edit] $\ge 2$

 

[e2m2a]

Are the restrictions going to come in one at a time or is there a complete problem description ?
'Integers' is quite a bit more than 'natural numbers > 2'

Interested only in positive integers or natural numbers for s > 1,

 

[mfb]

A solution to C²² = A²² + B¹¹ would be a solution to D¹¹ = E¹¹ + B¹¹ where D = C² and E = A², which is impossible per Fermat's last theorem. Similar for all other positive integers s apart from 1.

 

[e2m2a]

A solution to C²² = A²² + B¹¹ would be a solution to D¹¹ = E¹¹ + B¹¹ where D = C² and E = A², which is impossible per Fermat's last theorem. Similar for all other positive integers s apart from 1.

Ok. That makes sense. Thanks.