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On a coprime factorization of square triangular numbers. (English)
Int. J. Math. Educ. Sci. Technol. 27, No. 6, 883-891 (1996).
The square roots of square triangular numbers, $U_n$, are split into two special coprime factors called the ‘major’ and the ‘minor’ factor, denoted by $μ_n$ and $λ_n$. These factors on their own form two distinct sequences. Explicit formulae for $μ_n$ and $λ_n$ are established, in purely algebraic form as well as in hyperbolic function form. A large number of sundry properties of $μ_n$ and $λ_n$ are established. Finally, an application of Major factors in obtaining a reduction formula for $U_n$ is demonstrated. (orig.)
Classification: F60
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