Question

Let x and y be consecutive integers. Suppose m be the number of solutions of $x^3-y^3=3k^2$ and n be the number of solutions of $x^3-y^3=2t^2$ , where k, t are integers. Then m + n equals:

• A. 13
• B. 5
• C. 6
• D. none of these

Answer 1

The correct option is D none of these

Let x=y+1 so, $x^3-y^3=1+3y(y+1)$ clearly this is not divisible by either 2 or 3 so m = 0 and n = 0 so m+n=0.
Hence option (d)