Factorial, Quadratic and Cubic
Equality Expressions Generator

How the equality works

Q(d) = d² is the quadratic value; C(d) = d³ is the cubic value. Thus −C(1) + Q(2) = −1 + 4 = 3. The same digit sequence, 12, occurs in order on both sides.

Each digit on the right may be assigned Q or C according to the selected option. The search tests every parenthesization with addition, multiplication, and subtraction in either direction. Negative intermediate values are allowed. No division is used. Each expression is verified exactly.

Verified examples

Select an example to search its digit sequence and result.

Choose result values

Set the interval for the value of both expressions. Leave the digit seed blank to try selected digit sequences automatically, including repeated digits.

Automatic search uses nonzero digits 1–9, including repetitions. Searching 2–4 digits with both limits set to all checks every Q/C choice and supported arithmetic form. Five and six digits have far more combinations: these modes require a limit of 1–100 equalities per sequence and a total limit of 1–5,000, so their results are partial. Choose “5 digits only” or “6 digits only” to reach those lengths without searching shorter sequences first. A single digit seed may have 2–6 digits. The result interval is inclusive. TXT and Excel include all found rows; the screen shows the first 200.