# Understand the problem

Find all positive integers that have 4 digits, all of them perfect squares, and such that is divisible by 2, 3, 5 and 7.

##### Source of the problem

Centroamerican olympiad 2016

##### Topic

Number theory

##### Difficulty Level

Easy

##### Suggested Book

An Excursion in Mathematics

# Start with hints

Do you really need a hint? Try it first!

Note that the digits can only be 0,1,4,9. Also, the last digit has to be 0.

The sum of the digits has to be divisible by 3. Hence (checking by hand), the possible candidates are 1110,1140,1410,4410,4140,9000,9090,9900 and 9990. Note that the two initial examples were 1110 and 9000. The other ones came by replacing one or more the digits with other digits that are equivalent modulo 3.

Check for multiples of 7 in the list.

The answer is 4410.

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#### Math Olympiad Program

Math Olympiad is the greatest and most challenging academic contest for school students. Brilliant school students from over 100 countries participate in it every year. Cheenta works with small groups of gifted students through an intense training program. It is a deeply personalized journey toward intellectual prowess and technical sophistication.

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