Question

一个自然数a若恰好等于另一个自然数b的平方,则称自然数a为完全平方数.已知a=2002²+2002²

Answer 1

a=2002^2+2002^2×2003^2＋2003^2

=2002^2+2002^2×(2002+1)^2＋(2002+1)^2

=2002^2+2002^2×(2002^2+2×2002+1)+2002^2+2×2002+1

=2002^2+2002^4+2×2002^3+2002^2+2002^2+2×2002+1

=2002^4+2×2002^3+3×2002^2+2×2002+1

=2002^4+2×2002^3+2002^2+2×2002^2+2×2002+1

=(2002^2+2002)^2+2×(2002^2+2002)+1

=(2002^2+2002+1)^2

=【2002（2002+1）+1】^2

=(2002x2003+1)²

得证

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