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How many positive integers $n$ satisfy $127 \equiv 7 \pmod{n}$? $n=1$ is allowed.

 Apr 29, 2018
 #1
avatar+971 
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Hey RB!

 

If \(127 \equiv 7 \pmod{n}\), then n is a divisor of 127 - 7 = 120.

 

The prime factorization of 120 is \(2^3 \cdot 3 \cdot 5\)

 

which has \((3 + 1)(1 + 1)(1 + 1) = 16\) positive divisors.

 

Therefore, there are 16 possible values of n.

 

I hope this helps,

 

Gavin.

 Apr 30, 2018

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