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Theorem four-square-mod-zero

i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, ≡mod(0, i, j0), ≡mod(0, i1, j0), ≡mod(0, i0, j0), ≡mod(0, i2, j0), prime(j), j0 < j, 1 < j, 0 < j, 0 < j0, 0 ≤ j, j ≠ 2, j0 ≠ 1 ⊦

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