x + 1/x = 3, and the Ladder to x⁵ + 1/x⁵
One condition, a two-line recurrence, and the fifth power falls out as a clean 123 with no radicals left. Climb the same ladder far enough and the golden ratio and the Lucas numbers are hiding underneath.
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Which Polynomials Map ℚ Onto ℚ? The Complete Answer
A line with rational coefficients maps ℚ onto ℚ. Nothing curved ever does. Three filters — interpolation, shape, denominators — leave the full classification.