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2. Prove the following statement by induction [3 marks]. For all nonnegative integers n, 3 divides no + 5n + 1. State the mathematical induction and show your work clearly. [6 marks] Upload File 3. Students are required to create 5 or 6-character long passwords to access the library. The letters must be from lowercase letters or digits. Each password must contain at most two lowercase letters and contains no repeated digits. How many valid passwords are there? You are required to show your work step-by-step