adv. math problem 2

Need help in determining the following proof exercise. (See attached file for full problem description) --- 4. Let f:Z+ --> Z be the function defined by... ---

Advanced math problem

1. Let d; a; b; r, and q be integers. a) Suppose that d|a and d|b. Show that d|(ra + qb). b) Suppose a = qb + r. Show that the set of common divisors of a and b is the set of common divisors of b and r.

Advanced math problem

1. Let a, b be positive integers, and write a = qb + r, where q, r are Elements of Z and 0 (= or)< r < b. Suppose that d = gcd(a, b). a) If r = 0 show that d = b. b) If r > 0 show that d = gcd(b, r). 4. Use Problem 1 to find: a) gcd(100; 3); b) gcd(100; 82).

Advanced math prblm

Let p and a be positive integers and suppose that p|a2. a) Show that p|(ra + sp)2 for all integers r; s. b) Use part a), the definition of prime integer, and Theorem 15.1.1 to construct a proof by induction that p|a. [Hint: If a (< or =) p consider p = qa + r, where 0 (< or =) r < a. If p < a consider a = qp + r, where 0 (< or =) r < p.] Theorem 15.1.1: The division theorem Let a and b be integers with b> 0. Then there are unique integers q and r such that a= bq+r and 0(< or =) r < b.

a SU do ku puzzles

please give the missing digit : it is a three by three puzzles, the first row has a 9and 7 ,but missing a first number, the second row has a 4, missing the first and third number and the last row is empty. the second thre by three square has a 3 in the first row,second row is empty, and third row has a 7 in the first box and 1 in the last box. the last three by three box has a 1 and 6 inthe first row, the last box is empty