MathDB

Let

n\geq 2

be a positive integer. Find the minimum value of positive integer

m

for which there exist positive integers

a_1,\ a_2,\ \cdots, a_n

such that :

\bullet\ a_1<a_2<\cdots <a_n=m

\bullet \ \frac{a_1^2+a_2^2}{2},\ \frac{a_2^2+a_3^2}{2},\ \cdots,\ \frac{a_{n-1}^2+a_n^2}{2}

are all square numbers.

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