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Consider the first 10 square numbers 1, 4, 9, 16 25, 36, 49, 64, 81 and 100. (1) Compute the number of the positive divisors

Consider the first 10 square numbers 1, 4, 9, 16 25, 36, 49, 64, 81 and 100. (1) Compute the number of the positive divisors (factors) of each of them. (2) Make an educated guess based on your observation from part (1) as conjecture on the relation between a square number and the number of its positive divisors. (3) Prove your conjecture in part (2).

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