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Number Theory Level 3

Determine the number of ordered pairs of positive integers ( a , b ) (a, b) satisfying the equation 100 ( a + b ) = a b − 100 100(a + b) = ab - 100 . (Note: As an illustration, (1, 2) and (2, 1) are considered as two distinct ordered pairs.)


The answer is 18.

S P by s p , 16, India

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1 solution

X X
Jul 25, 2018

a b − 100 a − 100 b = 100 , a b − 100 a − 100 b + 10000 = 10100 = ( a − 100 ) ( b − 100 ) ab-100a-100b=100,ab-100a-100b+10000=10100=(a-100)(b-100) ,

so the thing we have to do is to find the number of positive divisors of 10100 10100 ,which is 18 18

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