Constraint programming models solving

Questions
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1

Hi
Can Mathematica solve mixed constraint programming models that include interval data for variables and different types of constraints?
Are there any examples of such constraints for Number theory tasks?
Like x^4+y^4+z^4=t^4 with conditions on x, y, z, t
Web versions to test.

2

There is FindInstance:


    FindInstance[x^4 + y^4 + z^4 == t^4 , {x, y, z, t}, PositiveIntegers]



    {{x -> 18796760, y -> 2682440, z -> 15365639, t -> 20615673}}

Minimize and Solveand a few other functions can also pop out AN answer.

If the problem is small enough, Solve with various constraints may do what you want.

Reduce can be useful for finding a possible algorithm to search for answers as well.

For deeper number theory functionality, it may be necessary to write your own algorithms.