KVPY SA Exam 2012 Question Paper

Question : 14 of 80

Marks: +1, -0

How many ordered pairs of (m,n) integers satisfy

m/12={12/n}

Solution:

m/12={12/n}

⇒mn=144

We want to find here total number of divisors of 144

144 = 2^4 . 3^2

Total divisors are (4 + 1) (2 + 1) = 15
But negative pairs are also possible hence = 30

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