We define the Ulam numbers by setting u1= 1 and u2 = 2. Furthermore, after determining whether the integers less than n are Ulam numbers, we set it equal to the next Ulam number if it can be written uniquely as the sum of two different Ulam numbers. Note that u3 = 3, u4 = 4, u5 = 6, and u 6 = 8.
a) Find the first 20 Ulam numbers.
b) Prove that there are infinitely many Ulam numbers.
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