Publish Date:
Consider the number 15.
There are eight positive numbers less than 15 which are coprime to 15: 1, 2, 4, 7, 8, 11, 13, 14.
The modular inverses of these numbers modulo 15 are: 1, 8, 4, 13, 2, 11, 7, 14
because
1 · 1 mod 15=1
2 · 8=16 mod 15=1
4 · 4=16 mod 15=1
7 · 13=91 mod 15=1
11 · 11=121 mod 15=1
14 · 14=196 mod 15=1
Let I(n) be the largest positive number m smaller than n-1 such that the modular inverse of m modulo n equals m itself.
So I(15)=11.
Also I(100)=51 and I(7)=1.
Find ∑ I(n) for 3≤n≤2×107
Press F12 and use the "Console" tab to view the output of your codes.