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## Saturday, October 29, 2011

### M381 - Challenge Exercise

In the Open University course Number Theory and Mathematical Logic the additional exercises sections of the workbooks are complemented with several 'challenge exercises'. This is one of them.

Let $n$ be an odd positive integer.
Prove that there are $\tau(n)$ ways of writing $n$ as a sum of consecutive positive integers.
For example, if $n=9$, $\tau(9)=3$ because $9$ has three divisors $1,3,9$ and the three sums are: $9$, $4+5$ and $2+3+4$.

To be continued.

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
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My continuous mission
To uncover hidden structures
To create new theorems and proofs
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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)