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Let N N be the number of ordered pairs of integers ( a , b ) (a,b) with a , b 2014 |a|,|b|\le 2014 such that lcm ( a , 2014 ) gcd ( b , 2014 ) = a . \frac{\text{lcm}(a,2014)}{\gcd(b,2014)}=a. Find the remainder when N N is divided by 1000 1000 .


The answer is 976.

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