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The Maxima on-line user's manual

Algebra Calculator

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Power_mod Calculator

Power_mod

Function: power_mod (<a>, <n>, <m>) Uses a modular algorithm to compute a^n mod m where <a> and <n> are integers and <m> is a positive integer. If <n> is negative, inv_mod is used to find the modular inverse.

p:47;
q:59;
n:p*q;
phi_n: (p-1)*(q-1);
e:79;
gcd(e,phi_n);
d:inv_mod(e,phi_n);
m:65;
c:power_mod(m,e,n);
power_mod(c,d,n);

          (%i1) power_mod(3, 15, 5);
          (%o1)                          2
          (%i2) mod(3^15,5);
          (%o2)                          2
          (%i3) power_mod(2, -1, 5);
          (%o3)                          3
          (%i4) inv_mod(2,5);
          (%o4)                          3

(%o1)                                true
(%i2) 

Power_mod Example

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