Input: 
n=integer to be tested 
a=element in Z_n^*

Output:
If n-1=m2^k
Then the program prints
b=a^m  mod n
and all the successive squarings b^2 b^2*b^2...b^{2^k}=b^{2^k-1}*b^{2^k-1} 



mrtest(n,a)=mu=0;m=n-1;\
while(lift(Mod(m,2))==0,mu=mu+1;m=m/2);\
print("emme=",m,",      ","mu=",mu,",             ");\
print("the basis is a=",a);\
print("n-1=2^",mu,"*",m);\
print("b=a^",m,"=",lift(Mod(a,n)^m));\
b=Mod(a,n)^m;\
for(j=1,mu,b=b^2;print("b^2^",j,"= ",lift(b)))  



Some Carmichael numbers

561
1729
2465
2821
6601
41041
825265
321197185
9746347772161
60977817398996785	
87674969936234821377601
32809426840359564991177172754241
12758106140074522771498516740500829830401
2333379336546216408131111533710540349903201