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Since when m=n, no any non-negative integer solution is found for any ( k = k 1 , k 2 , ..., k n) of this system, we call the non-negative integer solution of m=n+1 case as ideal non-negative integer solution...
As a specical solution, if all {a i, b i} are primes, we call this prime solution of m=n+1 case as ideal prime solution...
In these pages, we will only consider integral, non-trivial, primitive solutions of the above system.