# Understand the problem

find all integers such us is a perfect square.

##### Source of the problem

New Zealand team training 2004

##### Topic

Number Theory

##### Difficulty Level

Medium

##### Suggested Book

An Excursion in Mathematics

# Start with hints

Do you really need a hint? Try it first!

Try to show that the given expression (or a suitable multiple of it) lies between two consecutive squares.

Depending on the value of , there are two possibilities: and . Find out the conditions under which each inequality is valid.

Show that, for , none of the inequalities in the previous hint hold.

Verify that the only solutions are .

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# Connected Program at Cheenta

#### 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.