KVPY 2020-21 SA Exam Previous Papers

Question : 63 of 80

Marks: +1, -0

The number of ordered pairs (x, y) of integers satisfying

x^3 + y^3 = 65

Validate

Solution:

x^3 + y^3 = 65

Let x, y > 0
Clearly (1, 4) and (4, 1) holds for x or y ≥ 6 difference of two cubes is always greater than or equal to 91.
Hence only 2 ordered pair possible.

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