Mathematics Integers Assignment

1. Suppose that nEN and that b,a,..., a., C., C., are integers such that b|a, for each
   B/ai for each I=1,,,,,n
   Prove (by induction on n) that b divides ?aici. [25 marks]
2. 1. Find the set {a EZ: a²+1 is prime), explaining your answer.
   2. Use the Maple command is prime to find (a Z: 1a100 and a²+1 is prime). (You can either write down the Maple command(s) you did, or include a print-out of your Maple.)
   3. Set N to be your student ID number. Find (a Z: N+1a N+100 and a+1 is prime). [25 marks]

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