How can I solve this using bigmod method?
If the series is 1+a+a^2+a^3+a^4+a^5 then this will be equal to (1+a^2+a^4)+a(1+a^2+a^4). How can I apply bigmod here!
BigMod : This is for calculating the mod of a large number like 2^100 or 10^18.
long long bigmod(long long a, long long b, long long m)
{
if(b==0) return 1;
if(b%2==1)
{
long long p1 = a%m;
long long p2 = bigmod(a,b-1,m);
return (p1*p2)%m;
}
if(b%2==0)
{
long long h = bigmod(a,b/2,m);
return (h*h)%m;
}
}
I think BigMod is what I call Binary Exponentiation, lets say $$$w_n = a^0+a^1+a^2\dots a^n$$$, what we will realize is that if $$$n$$$ is even then
otherwise
, so $w_n$ can be calculated using binary exponentiation.
1 + a^1 + a^2 + ... + a^d = ( a^(d+1)-1 ) /( a-1)
Here, you can compute the value of a^(d+1) mod m using bigmod,then subtract 1 from it.And then mutiply this with inverse modulo of (a-1) mod m.
Here a , d and m should be <= 10^18.
And how do you plan to get the inverse if m ain’t prime?
If m is not prime,we can use extended GCD function to find the inverse value.
What if it just plainly doesn't exist like a = 3, m = 4.
Yes,if m and a-1 are not co-prime then maybe we can't use this formula :(