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Problem 793

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Median of Products

Let $S_i$ be an integer sequence produced with the following pseudo-random number generator:

• $S_0=290797$
• $S_{i+1}=S_i^{2}mod50515093$

Let $M(n)$ be the median of the pairwise products $S_i{S}_j$ for $0\le i<j<n$.

You are given $M(3)=3878983057768$ and $M(103)=492700616748525$.

Find $M(1000003)$.

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乘积的中位数

记$S_i$为由如下伪随机数生成器给出的整数列：

• $S_0=290797$
• $S_{i+1}=S_i^{2}mod50515093$

对于任意$0\le i<j<n$，记$M(n)$为所有乘积$S_i{S}_j$的中位数。

已知$M(3)=3878983057768$，$M(103)=492700616748525$。

求$M(1000003)$。

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