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. 
  






 
      <br />
<table width="100%"><tr><td align="center">
    <math xmlns="http://www.w3.org/1998/Math/MathML">
    <mstyle displaystyle="true"><mrow>
<mtable >
<mtr><mtd  columnspan="1"><mrow><mi>a</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow>
</mtd><mtd >
<mrow><mo>=</mo></mrow>
</mtd><mtd >
<mrow><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi></mrow>
</mtd></mtr>
<mtr><mtd  columnspan="1"><mrow><mi>b</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow>
</mtd><mtd >
<mrow><mo>=</mo></mrow>
</mtd><mtd >
<mrow>
<msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow>
</msup>
<mo>+</mo>
<msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow>
</msup>
<mo>+</mo>
<msup><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow>
</msup>
<mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo>
<msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow>
</msup>
</mrow>
</mtd></mtr>
<mtr><mtd  columnspan="1"><mrow><mi>c</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow>
</mtd><mtd >
<mrow><mo>=</mo></mrow>
</mtd><mtd >
<mrow>
<msup><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow>
</msup>
<mo>+</mo>
<msup><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow>
</msup>
<mo>+</mo>
<msup><mrow><mn>3</mn></mrow><mrow><mn>3</mn></mrow>
</msup>
<mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo>
<msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow>
</msup>
<mo>.</mo></mrow>
</mtd></mtr>
</mtable>
</mrow>
    </mstyle></math>
</td></tr></table>
<br />


<!---->
  It is well known that c = a <sup>2</sup> . What are the
  relationships between a and b and between b and c? <br />