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Problem #PRU-116021

Problems Algebra Algebraic inequalities and systems of inequalities Number inequalities. Number comparison

Find the largest natural number $n$ which satisfies $n^{200} < 5^{300}$ .

Problem #PRU-35052

Problems Algebra Algebraic inequalities and systems of inequalities Classical inequalities Probability and statistics Probability theory Discrete distribution Number inequalities. Number comparison

There are 30 students in the class. Prove that the probability that some two students have the same birthday is more than 50%.