Question

3. Thabit ibn-Qurra provides a formula for amicable numbers: If p 3.22 -1,q 3-2-11, and 9-22n-1-1 are odd primes, then 2"pq and 2"r are amicable. (a) Let n -2. Show that the resulting numbers are amicable. This is the smallest pair of amicable numbers. (b) In 1866 a 16-year-old Italian 7discovered the second smallest pair: 1184 - 25.37 and 1210-2.5 112 Show that this pair is also amicable. Does this pair arise from Thabit's formula?

Answer 1

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