[ February 1, 2026 ] [ Last update [ -- ]
Polynomial equation with ninedigital coëfficients.
By Alexandru Petrescu

Let N = abcdefghi be a ninedigital number.

Let S₁ = abc, S₂ = def and S₃ = ghi

Now let us consider the following polynomial equation

x³ – S₁*x² + S₂*x – S₃ = 0

This equation has 3 integer roots (solutions)
only for ninedigital number   134895762
with S₁ = abc = 134, S₂ = deg = 895 and S₃ = ghi = 762

namely x₁ = 1, x₂ = 6 and x₃ = 127

So we have a new, interesting and unique ninedigital number !

A curiosity for the fans 1 + 6 + 127 = 134 which is S₁ or abc