@VR_9781959 wrote:
I am looking to expand the result i,e the vector:answer in the example would be of seven integers
Seven? If you really mean only integer solutions, the result must be a vector of 15 values!!

But you sure can limit the solutions to positive integers if thats what you are looking for:

Unfortunately the above only works in real Mathcad and in Prime up to version 6 (if you chose to use the "Legacy Symbolic Engine", muPad). The new engine built into Prime 7 (Axiom) is less capable than the older one (which in no way was state of the art, either). Here is what you see when you use the new engine:

Correct and disappointing at the same time.
-Also, is it possible to define a number to an integer?
Only with assume when you use the symbolic engine, as you have just seen. And very often this modifier is simply ignored by the engine. Prime is not an appropriate tool for diophantic equations.