For an integer $m>1$, it is shown that each congruence class modulo $m$ contains infinitely many congruent numbers whose associated elliptic curves have rank at least two.

The first $q$-Painlevé equation has a unique formal solution around the infinity. This series converges only for $|q|=1$. If $q$ is a root of unity, this series expresses an algebraic function. In cases that all coefficients are integers, it can be represented by generalized hypergeometric series.