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HMMT November

Number theory Difficulty 4.8 AIME Find the answer

Call an integer n>1n>1 radical if 2n−12^{n}-1 is prime. What is the 20th smallest radical number? If AA is your answer, and SS is the correct answer, you will get max⁡(25(1−∣A−S∣S),0)\max \left(25\left(1-\frac{|A-S|}{S}\right), 0\right) points, rounded to the nearest integer.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

The answer is 4423.

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