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# NUMBER THEORY CHALLENGE

If x^2-px-q=0, where p and q are positive integers, which of the following could not equal x^3?

A 4x+3 B 8x+5 C 8x+7 D 10x+3 E 26x+5

Note by Naheem Ahmed
3 years, 7 months ago

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$$x^{2}=px+q$$

$$x^{3} =x(px+q) =px^{2}+qx =p(px+q)+qx =x(p^{2}+q)+pq$$

Hence there must exists two integers p and q satisfying above condition

A) p=1, q=3

B) No p and q exists (Answer)

C) p=1, q=7

D) p=3, q=1

E) p=5, q=1

- 3 years, 7 months ago