Y by Adventure10, Mango247
Let
be a function from the set of real numbers
into itself such for all
we have
and
![\[ f \left( x + \frac{13}{42} \right) + f(x) = f \left( x + \frac{1}{6} \right) + f \left( x + \frac{1}{7} \right).\]](//latex.artofproblemsolving.com/2/6/c/26c7c7f145ed934ef356476943dea07074691093.png)
Prove that
is a periodic function (that is, there exists a non-zero real number
such
for all
).




![\[ f \left( x + \frac{13}{42} \right) + f(x) = f \left( x + \frac{1}{6} \right) + f \left( x + \frac{1}{7} \right).\]](http://latex.artofproblemsolving.com/2/6/c/26c7c7f145ed934ef356476943dea07074691093.png)
Prove that



