(\frac{187}{523})=(\frac{11}{523})(\frac{17}{523})=(\frac{523}{11})(\frac{523}{17})=(\frac{6}{11})(\frac{13}{17})=(\frac{2}{11})(\frac{3}{11})(\frac{13}{17})=-(\frac{11}{3})(\frac{17}{13})=-(\frac{2}{3})(\frac{4}{13})=(\frac{2}{13})(\frac{2}{13})=1