Question 7

(a) Let m, n be positive integers. If $$m^3+n^3$$ is the square of an integer, then prove that $$(m+n)$$ is not a product of two different prime numbers. (b) a, b, c are real numbers such that $$ab+bc+ca=-1$$. Prove $$a^2+5b^2+8c^2 \ge 4$$.


Correct Answer: part_a=0 part_b=4

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