Euler's Sum of Powers Conjecture - Generalizations

Generalizations

In 1967, L. J. Lander, T. R. Parkin, and John Selfridge conjectured that if, where a_i ≠ b_j are positive integers for all 1 ≤ i ≤ n and 1 ≤ j ≤ m, then m+n ≥ k. This would imply as a special case that if

(under the conditions given above) then n ≥ k−1.