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sovle x*36 = 216 if a*(b*c) = (a*b)c$ and $a*a = 1$

Source: 1993 Swedish Mathematical Competition p4

April 2, 2021

algebraequation

Problem Statement

To each pair of nonzero real numbers

a

and

b

a real number

a*b

is assigned so that

a*(b*c) = (a*b)c

and

a*a = 1

for all

a,b,c

. Solve the equation

x*36 = 216