Prove that there exists a convex 1990-gon with the following two properties :
a.) All angles are equal.
b.) The lengths of the 1990 sides are the numbers
![1^2](/media/m/9/6/a/96a073bdca9b3f195e701ae0f040a143.png)
,
![2^2](/media/m/c/5/5/c55c88a5d1b0a676ac9309f321033e7a.png)
,
![3^2](/media/m/f/9/4/f94fb1142655363cc2c62236916038dd.png)
,
![\cdots](/media/m/3/b/3/3b3f59fde5e3bfd745da44e4db64f7e5.png)
,
![1990^2](/media/m/b/5/e/b5e7903934fc094dc80b750c4818e70e.png)
in some order.
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Prove that there exists a convex 1990-gon with the following two properties :
a.) All angles are equal.
b.) The lengths of the 1990 sides are the numbers $1^2$, $2^2$, $3^2$, $\cdots$, $1990^2$ in some order.