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Find all n such that n^4+6n^3+11n^2+3n+31 is perfect square.

Source: 2007 Newton Math Competition Team Questions #5

March 17, 2007

Problem Statement

Find all n such that n4+6n3+11n2+3n+31n^{4}+6n^{3}+11n^{2}+3n+31 is a perfect square.