KVPY SA Exam 05-Nov-2017 Question Paper

Question : 4 of 80

Marks: +1, -0

Let S be the set of all ordered pairs (x, y) of positive integers satisfying the condition

x^2 -y^2 = 12345678

. Then

Solution:

x^2 -y^2 = 12345678 (x, y ∈ I^{+})

R.H.S. is even, so x, y should be odd integer
but difference of square of two odd integers is
multiple of 8 but R.H.S. is not multiple of 8

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