#1757 · Algebra · Polynomials

Homogeneous products of three variables

Prove that the sum of the homogeneous products of $n$ dimensions which can be formed of the letters $a, b, c$ and their powers is $\frac{a ^{n + 2} ( b - c ) + b ^{n + 2} ( c - a ) + c ^{n + 2} ( a - b )}{a ^{2} ( b - c ) + b ^{2} ( c - a ) + c ^{2} ( a - b )} .$

~20 minProof · checked by AIgenerating functionspartial fractionssymmetric polynomials

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXIII. Partial Fractions, Examples XXIII, No. 26

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