A Tough one

[harsh.champ]

Let x and y be consecutive integers. Suppose m be the number of solutions of x3 − y3 = 3k2 and n be the number of solutions of x3 − y3 = 2t2, where k, t are integers. Then m + n equals:

(1)31
(2)13
(3)5
(4)6
(5)None of the above

[ajith]

Let x and y be consecutive integers. Suppose m be the number of solutions of x3 − y3 = 3k2 and n be the number of solutions of x3 − y3 = 2t2, where k, t are integers. Then m + n equals:

(1)31
(2)13
(3)5
(4)6
(5)None of the above

(x-y)(x^2+y^2+xy) = 3k2

x^2+y^2+xy = 3k2


(9^2) + (8^2) + (9 * 8) = 217

(10^2) + (9^2) + (10 * 9) = 271

(11^2) + (10^2) + (10 * 11) = 331

(11^2) + (12^2) + (12 * 11) = 397

So it is evident that there is no solution for both the equations m = 0 n=0

I go for E

[Mom4MBA]

Didn't get the question nor the answer...............anybody else with the explanation.