Competition problem — Number theory

Library / /10 of 841

Number theory Difficulty 4.5 AIME Find the answer

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

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

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.