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1.) Let a and b be intgers where b is not equal to 0. Suppose that the quadratic equation x^2+ax+b=0 has solutions z and w. If z is part of set Z and w is part of set Z, show that z divides b and w divides b.

For questions 2, 3, 4, let N=(a sub n)(a sub n-1)...(a sub 2)(a sub 1)(a sub 0) be a part of set N

2.) Prove that N divides 4 <-> (a sub 1)(a sub 0) divides 4, where (a sub 1)(a sub 0) denotes the natural number formed by the last 2 digits of N

3.) Prove that N divides 8 <-> (a sub 2)(a sub 1)(a sub 0) divides 8 where (a sub 2)(a sub 1)(a sub 0) denotes the natural number formed by the last 3 digits of N

4.) Use questions 2 and 3 to deduce that if (a_1)(a_0) divides 4 then (2(a_1)(a_0)) divides 8

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