(This is actually a fairly common homework problem, thus how to compute such a modulus of a power too large to compute directly using doubles.)
Since you asked about vpi, it is simple. Use powermod, the tool designed to solve exactly that problem.
powermod(188,80,34969)
ans =
14961
As a test:
mod(vpi(188)^80,34969)
ans =
14961
Of course, the second solution is much slower, since there vpi was forced to compute the full number, then compute the modulus.
Note that you COULD have done the computation using nothing more than doubles.
B = flip(dec2bin(80))
B =
'0000101'
Bi = find(B == '1') - 1
Bi =
4 6
So we see that 80 (the exponent) can be written as 80=16+64.
Therefore, 188^80=188^16*188^64
Eventually, you would compute the modulus as:
mod(2993*11969,modulus)
ans =
14961
So you can actually compute a powermod in double precision as long as the modulus is no larger than sqrt(2^53 - 1).
