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Problems in eighth grade mathematics
1, equation x2+xy+y2=29 The number of integer solutions (x, y) about x and y is

2. It is known that a 1, a2, a3, a4 and a5 are five different integers satisfying the condition a 1+a2+a3+a4+a5=9. If b is the equation about x (X-A 1) (X-A2) (X-A3) (X-A4).

3. The three vertices A, B and C of 3.RT △ ABC are all on the parabola y=x? The hypotenuse AB is parallel to the x axis. If the height on the hypotenuse is h, find the value range of h.

4. Take n different numbers from the continuous natural number 1, 2, 3, …, 2008.

(1) Verification: When n = 1007, the sum of four numbers always exists equal to 4017 no matter how to select n numbers;

(2) When n≤ 1006(n is a positive integer), does the above conclusion hold? Please explain the reason.

5. Line segments whose lengths are all integer centimeters: a 1, a2, a3, a4, a5, a6, a7 satisfy A 1 < A2 < A3 < A4 < A5 < A6 < A7, and any three of these seven line segments cannot form a triangle. If A 1 = 6544,