满足x²-y²=2011的整数对(x,y)的组数是

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满足x²-y²=2011的整数对(x,y)的组数是满足x²-y²=2011的整数对(x,y)的组数是满足x²-y²=2011的整数对(x,y

满足x²-y²=2011的整数对(x,y)的组数是
满足x²-y²=2011的整数对(x,y)的组数是

满足x²-y²=2011的整数对(x,y)的组数是
2011是质数,2011=1*2011=-1*(-2011)
x²-y²=(x+y)(x-y)
分别对应相等可得(1006,1005)(1006,-1005)(-1006,1005)(-1006,-1005)四组