1. Integers x and y such that x^3 -y^3 not = n^3 for any natural number n

2 for any non zero integers a and b there is a rational number r such that a +b= r^2

3 there is a unique pair of nowhere x and y such that x^2 + y^2 =7^2

1 choose x=2 and y =0 then x^3 -y^3 = 2^3

2. choose a=1 and b =1 then a+b =2 and r^2 =2 with rational r not possible

3. choosing x=7 and y=0 or x=0 and y =7 will get you the same result

x^2 +y^2 = 7^2

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