Competition problem — Number theory

Library / /9 of 860

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. Spacing and $ signs are ignored.

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 and solution reproduced as published; topic and difficulty added by this site.