How many positive integers $n$ satisfy $127 \equiv 7 \pmod{n}$? $n=1$ is allowed.
How many positive integers \(n\) satisfy \(127 \equiv 7 \pmod{n}\)? n=1 is allowed.
I am just thinking on paper - not sure where it will go.
factor(127) = 127 so 127 is a prime number and so is 7
127 = 7(mod 120)
120=0(mod n)
so n is a factor of 120 i think
factor(120) = (2^3*3)*5
What factors are bigger than 7
8, 10, 12, 15, 20, 24, 30, 40, 60, 120
So the answer is 10 That is if n is a positive.