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How many positive integers, a, are there such that 2027 divided by a leaves a remainder of 7?
 Aug 15, 2013
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2027 mod a = 7
=> 2020 mod a = 0
=> gcd(2020,a) != 1
2020 = 2^2*5*101
So we have to calculate all combinations with 2^2*5*101 (=3^2):
2*5
2*101
2*5*101
2*2*5
2*2*5*101
101
5*101
2*2*101
2*2 <- less than 7, but a must be greater than 7

Ergo: There are 8 positive integers of a so that 2027 mod a = 7
 Aug 17, 2013

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