2021 AIME I Problems/Problem 3

Problem

Find the number of positive integers less than $1000$ that can be expressed as the difference of two integral powers of $2.$

$\binom{11}{2} = 55$ We need to subtract 5 since $2^{10} - 2^0, 2^1, 2^2, 2^3, 2^4$ don't work. $55-5=\boxed{050}$ ~hansenhe

2021 AIME I (Problems • Answer Key • Resources)
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