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Unformatted text preview: j m j j n j . Dene sequences j n j > n 1 > n 2 and q 1 ;q 2 ;::: by induction, as follows. Dene q 1 and n 1 as the quotient and remainder upon dividing m by n : m D q 1 n C n 1 and n 1 < j n j : If n 1 > 0 , dene q 2 and n 2 as the quotient and remainder upon dividing n by n 1 : n D q 2 n 1 C n 2 and n 2 < n 1 : In general, if n 1 ;:::;n k 1 and q 1 ;:::;q k 1 have been dened and n k 1 > , then dene q k and n k as the quotient and remainder upon dividing n k 2 by n k 1 : n k 2 D q k n k 1 C n k and n k < n k 1 :...
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 Fall '08
 EVERAGE
 Algebra, Integers

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