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Putnam 2016 A5

Source:

December 4, 2016

PutnamPutnam 2016Putnam algebra

Problem Statement

Suppose that

G

is a finite group generated by the two elements

g

and

h,

where the order of

g

is odd. Show that every element of

G

can be written in the form

g^{m_1}h^{n_1}g^{m_2}h^{n_2}\cdots g^{m_r}h^{n_r}

with

1\le r\le |G|

and

m_n,n_1,m_2,n_2,\dots,m_r,n_r\in\{1,-1\}.

(Here

|G|

is the number of elements of

G.

)

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