Maths Olympiad Exam

Find the number of 4-digit numbers(in base 10) having non-zero digits and which are divisible by 4 but not by 8.

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Maths Olympiad Other Question

Let P1(x) = ax^2 + bx + c, P2(x) = bx^2 + cx +a, P3(x) = cx^2 + ax + b be three quadratic polynomials where a, b, c are non-zero real numbers. Suppose there exists a real number
such that P1() = P2() = P3(). Prove that a = b = c. Find three distinct positive integers with the least possible sum such that the sum of the reciprocals of any two integers among them is an integral multiple of the reciprocal of the third integer.