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On the almost universality of $\lfloor x^2/a\rfloor +\lfloor y^2/b\rfloor +\lfloor z^2/c\rfloor $
In 2013, Farhi conjectured that for each m ≥ 3, every natural number n can be represented as ⌊x 2 /m⌋ + ⌊y 2 /m⌋ + ⌊z 2 /m⌋ with x, y, z ∈ Z, where ⌊•⌋ denotes the floor function.Moreover, in 2015, Sun conjectured that every natural number n …