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integer system (has root? )

Source: 41-st Vietnamese Mathematical Olympiad 2003

March 10, 2007
number theory proposednumber theory

Problem Statement

Find the largest positive integer nn such that the following equations have integer solutions in x,y1,y2,...,ynx, y_{1}, y_{2}, ... , y_{n} : (x+1)2+y12=(x+2)2+y22=...=(x+n)2+yn2.(x+1)^{2}+y_{1}^{2}= (x+2)^{2}+y_{2}^{2}= ... = (x+n)^{2}+y_{n}^{2}.
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