Problem of the Day #75

POTD February 21, 2024

For polynomial P(x)=1-\dfrac{5}{3}x+x^{2}, define Q(x)=P(x) \cdot P(x^{3}) \cdot P(x^{5}) \cdot P(x^{7}) \cdot P(x^{9})=\sum\limits_{i=0}^{50} a_i \cdot x^{i}. Then \sum\limits_{i=0}^{50} |a_i|=\dfrac{m}{n}, where m and n are relatively prime positive integers. Find m+n.