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Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials.

$$\begin{eqnarray} a(n) &= &1 + 2 + 3 + ... + n \\ b(n) &= &1^2 + 2^2 + 3^2 + ... + n^2\\ c(n) &= &1^3 + 2^3 + 3^3 + ... + n^3. \end{eqnarray}$$

It is well known that $c = a^2$ . What are the relationships between $a$ and $b$ and between $b$ and $c$?

Relations. Making and proving conjectures. Generalising. Simultaneous equations. Mathematical reasoning & proof. Manipulating algebraic expressions/formulae. Creating expressions/formulae. Factorisation (algebraic). Summation of series. Polynomials.