mod problem 1

n=1; a=(127 % n);printa,n; n++; if(n<200, goto1, discard=0;

Rem  n
7       8
7       10
7       12
7       15
7       20
7       24
7       30
7       40
7       60

7       120

So, the ten numbers to the RHS.

How many positive integers n satisfy 127 = 7 mod n? (n=1 is allowed)

127=7modn

127=kn+7     where k and n are integers and n is bigger than 7

120 = kn

prime factors of 120 are 2^3 *3*5

So what factors are bigger than 7

3    too little

5    too little

3*5     =15

2*5    =10

2*15   =30

4*3    = 12

4*5   =20

4*15  =60

8*3    =24

8*5    =40

8*15  =120

127 = 7 mod n?

10, 12, 15, 20, 24, 30, 40, 60, 120 

So there are 9 of them   

Melody:

Also 127 mod 8 = 7