Consecutive Pythagorean triangle sides
SMRTR summary
Pythagorean triples are sets of three numbers that satisfy the equation for right triangles, and some special ones contain consecutive numbers. When two shorter legs are consecutive, the solutions follow a specific recurrence sequence (OEIS A001652), proven by George Osborne in 1914. When the longer leg and hypotenuse are consecutive — like (5, 12, 13) — Euclid's formula shows all solutions follow the pattern 2n(n+1).
SMRTR provides this summary for quick context. The original article belongs to John D. Cook.
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