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22. Prove that, for nonnegative integers n and k, pkn(npk)(modp). 23. (a) Let An denote the number of lattice paths from (0,0) to (n,n) using three kinds of steps : (1,0),(0,1), or (1,1). Show that An=k=0n(nk)(2nkn). (b) Show that n=0Anxn=(16x+x2)1/2. 22. Prove that, for nonnegative integers n and k, pkn(npk)(modp). 23. (a) Let An denote the number of lattice paths from (0,0) to (n,n) using three kinds of steps : (1,0),(0,1), or (1,1). Show that An=k=0n(nk)(2nkn). (b) Show that n=0Anxn=(16x+x2)1/2