number-theory / Experimental number theory

Sun's Conjecture 4.6(ii) on Trigonometric Permanents

For an odd prime $p$, do Sun's normalized trigonometric permanents satisfy $s_p < 0 \iff p \equiv 5 \pmod{12}$ and $s'_p < 0 \iff p \equiv 7 \pmod 8$? Exact computation at $p = 29$ refutes both sign laws.

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number-theoryJun 12, 2026Significance 5/100Registry: unreviewed

Sun's Conjecture 4.6(ii) on Trigonometric Permanents

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For an odd prime $p$, do Sun's normalized trigonometric permanents satisfy $s_p < 0 \iff p \equiv 5 \pmod{12}$ and $s'_p < 0 \iff p \equiv 7 \pmod 8$? Exact computation at $p = 29$ refutes both sign laws.

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For an odd prime $p$, do Sun's normalized trigonometric permanents satisfy $s_p < 0 \iff p \equiv 5 \pmod{12}$ and $s'_p < 0 \iff p \equiv 7 \pmod 8$? Exact computation at $p = 29$ refutes both sign laws.

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