2021 GCIME Problems
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Problem 1
Let denote the number of primes less than or equal to . Suppose . For some fixed what is the maximum possible number of solutions but not exceeding ?
Problem 2
Let denote the number of solutions to the given equation: What is the value of ?
Problem 3
Let be a cyclic kite. Let be the inradius of . Suppose is a perfect square. What is the smallest value of ?
Problem 4
Define as the harmonic mean of all the divisors of . Find the positive integer for which is the minimum amongst all .
Problem 5
Let be a real number such that If the value of can be expressed as where and are relatively prime positive integers, then what is the remainder when is divided by ?