Hello I'm having trouble solving the following question. How do I solve for it?

There are two players in the game. Each player can pick any integer number between 1 and n. If two numbers are the same then player 1 pays 1 dollar to player 2. If two numbers are different than nothing happens.

(a) Prove that there are no equilibria in pure strategies;

(b) Prove that in the equilibrium each strategy should be played with a positive probability.

(c) Find all NE of the game.