(\frac{187}{523})=-(\frac{523}{187})=-(\frac{149}{187})=-(\frac{187-149}{187})=-(\frac{28}{187})=-(\frac{2}{187})(\frac{19}{187})=(\frac{19}{187})=-(\frac{187}{19})=-(\frac{16}{19})=-(\frac{2}{19})(\frac{2}{19})(\frac{2}{19})(\frac{2}{19})= -1