Hello, can you please answer the following using discrete math concepts

4. Describe an efficient algorithm to find if there is an integer in an array A[1,n] of integers such that the number of times it appears in A is equal to its value. What is the big-O complexity of your algorithm? Would you use the same algorithm if all integers in the array are in the range 1100 ? Why? 5. A natural number is an Ulam number if it is 1 or 2 or it can be uniquely written as a sum of two different smaller Ulam numbers. For example: 3 is an Ulam number (3=1+2),4 is an Ulam number (4=1+3;2+2 is not llowed ); but 5=1+4=2+3 is not an Ulam number. Show that the set of Ulam numbers is infinite