Competition problem — Number theory

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Number theory Difficulty 4.1 AIME Find the answer United States

Problem:

How many multiples of $7$ between $10^{6}$ and $10^{9}$ are perfect squares?

Your answer

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

Solution

Solution:

$\left[\sqrt{\frac{10^{9}}{7^{2}}}\right] - \left[\sqrt{\frac{10^{6}}{7^{2}}}\right] = 4517 - 142 = 4375$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.