On the positivity of truncated pentagonal number series and some conjectures of Merca

Manjil P. Saikia, Abhishek Sarma

Let ${\nu }_2(m)$ denote the $2$-adic valuation of a positive integer $m$ and set $N_m=m(1+{\nu }_2(m)/2)$. We prove four conjectures of Merca on the nonnegativity of truncated pen…