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MathNet 2009-part-04 — 175 problems (EN–VI) Question 142

Math Olympiad Vault · MathNet 2009-part-04 — 175 problems (EN–VI)

Question 142

a) Consider the squares of the numbers $1$, $2$, $\ldots$, $2009$ written one after another in some random order as one number. Is it possible to obtain a perfect square of an integer in this way?

b) Consider the numbers $1$, $2$, $\ldots$, $2009$ written one after another in some random order as one number. Is it possible to obtain a perfect square of an integer in this way?