Thâbit ibn Kurrah's rules is a beautiful result of Thâbit ibn Kurrah dating back to the tenth century. Take n>=2 and suppose that h | = | 3·2^n - 1 t | = | 3·2^(n - 1) - 1 s | = | 9·2^(2n - 1) - 1 are all prime. Then (2^n h t, 2^n s) are an amicable pair, where h is sometimes called a Thâbit ibn Kurrah number. This form was rediscovered by Fermat in 1636 and Descartes in 1638 and generalized by Euler to Euler's rule.
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