Skip to the content

Putnam 1958 A4

Session A

If $a_{1}, a_{2}, \ldots, a_{n}$ are complex numbers such that $\left|a_{1}\right|=\left|a_{2}\right|=\cdots=\left|a_{n}\right|=r \neq 0$ and if ${ }_{n} T_{s}$ denotes the sum of all products of these $n$ numbers taken $s$ at a time, prove that $\left|\frac{{ }_{n} T_{s}}{{ }_{n} T_{n-s}}\right|=r^{2 s-n}$ whenever the denominator of the left-hand side is different from zero.

Dataset text PutnamGAP. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.

Similar problems

These problems have the most words in common with this statement.

Locator putnam/1958/a4 · Tag PFPMCQAJN3 · Edit this page on GitHub · Keys: j next, k previous