Algebra 1 HW 1

Algebra 1 HW 1 - (4 Suppose that u v = 1 Show that u v u...

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Homework assignment 1 Math 235 (Fall 2011) Due: Sept 14 (Wednesday) (1) Prove that for any n 1, x n y n =( x y )( x n 1 + x n 2 y + ··· + y n 1 ) . (2) Let a and b be nonzero integers such that b = aq + r ,where0 r<a .P rov etha t ( b, a )=( a, r
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Unformatted text preview: (4) Suppose that ( u, v ) = 1. Show that ( u + v, u − v ) is either 1 or 2. (5) Show that if n is not a prime, then n has a prime divisor ≤ √ n . Department of Mathematics, McGill University, Montreal, QC, H3A 2K6 Canada E-mail address : [email protected] 1...
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