3
$\begingroup$

Possible Duplicate:
Prove that all even integers $n \neq 2^k$ are expressible as a sum of consecutive positive integers

Some natural numbers can be expressed as a sum of consecutive natural numbers in more than one way. For example, $7$ can get expressed both as $7$, and $(3+4).$ In terms of a sum of consecutive numbers, $4$ and $8$ can only get expressed as $4$, and $8$ respectively. Call such numbers consecutive-primes. How many consecutive-primes exist? Given all previous consecutive-primes, is there a way to compute the next consecutive-prime?

  • 5
    The powers of $2$ are the only ones. The problem has been solved on this site, probably repeatedly. [Here is a link.](http://math.stackexchange.com/questions/59131/prove-that-all-even-integers-n-neq-2k-are-expressible-as-a-sum-of-consecutiv)2012-05-02

1 Answers 1

7

Only powers of 2 have exactly 1 odd divisor.

  • 1
    @DougSpoonwood Can you see how to use an odd divisor to create a sum of consecutive numbers? Hint: 3=0+1+22012-05-02