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For how many positive integers n such that 7n+1 is divisible by 3n+5?

 Jul 4, 2020
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If  n = 1,  (7n + 1)/(3n + 5)  =  1 

If  n = 9,  (7n + 1)/(3n + 5)  =  2.

 

The quotient  (7n + 1)/(3n + 5)  can never reach 3 because, as n approaches infinity,

the  lim (7n + 1)/(3n + 5)  = 7/3.

 

There are only two possibilities. 

 Jul 4, 2020

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