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Putnam 2012 A2

Source:

December 3, 2012

Putnamabstract algebragroup theorycollege contestsPutnam algebra

Problem Statement

Let

*

be a commutative and associative binary operation on a set

S.

Assume that for every

x

and

y

in

S,

there exists

z

in

S

such that

x*z=y.

(This

z

may depend on

x

and

y.

) Show that if

a,b,c

are in

S

and

a*c=b*c,

then

a=b.

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