Pan-Magic Algebraic Squares

The complete symbolic solution for an N×N square in which every row, every column and every diagonal — including the broken (wrapped) ones — sums to N·M. Cells shown in amber are the free parameters; the rest are forced.

Diagonals

Letters

Size

every 2×2 block = 4M (most-perfect) half-shift pairs = 2M associative (opposite pairs = 2M) every + and × pentad = 5M scale letters to integer coefficients

Pan-Magic Algebraic Squares

Check every line re-added symbolically

Numbers set the free parameters, get a square

Copy out