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HL IA I Divisibility

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Hey, I am wondering if anyone who has done the HL IA I for divisibility used induction (purely) to answer question 3 and 4. I used mainly arguments based around the choose function, becuase I can't see how it could be done purely with induction.

P.S. Who here thinks that it was a bad idea on the IBO's part in putting one of the most known theorems (where the proof is even in most IB books) into an IA?

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