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Let 
$\text{ }\!\!\lambda\!\!\text{ }\left( n \right)$ denote the Liouville function. Complementary to the prime number theorem, Chowla
conjectured that
*
$$\sum\limits_{n\le x}{\lambda \,\left( f\left( n \right) \right)}=o\left( x \right)$$
for any polynomial 
$f\left( x \right)$ with integer coefficients which is not of form 
$bg{{\left( x \right)}^{2}}$.
