# A question about inverse modulo a number.

If xy $$equiv$$ 1 (mod a), Can i write x $$equiv$$ $$frac{1}{y}$$ (mod a).

I was thinking about this while solving IMO 2005 P4, so can i write 2$$^{p-2}$$ + 3$$^{p-2}$$ + 6$$^{p-2}$$ $$equiv$$ $$frac{1}{2}$$ + $$frac{1}{3}$$ + $$frac{1}{6}$$ (mod p)