I am making operation in matlab, such as mod((11239388^375) , 751 ). However the result are NaN because 11239388^375 results inf. Is there anyway to make 11239388^375 results in integer? Thanks :D

Answer by Walter Roberson
on 4 Apr 2014

b = 11239388;

e = 375;

m = 751;

feval(symengine, 'powermod', b, e, m)

See also John's contribution as mentioned by Nitin, and see http://www.mathworks.com/matlabcentral/fileexchange/38516-powermod

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Answer by Ken
on 5 Apr 2014

Thanks Nitin and Walter :) I'll try that. However my program often run into busy state, either i set the breakpoint or not. Then I try part of the program, e.g. :

e=1;

p=753;

s=(p-1)/(2^e);

while mod(s,2) == 0

e=e+1;

s=(p-1)/(2^e);

end

When I put a breakpoint at "end", then I keep continue until I get the result e = 4 and s = 47. But when I just run the program without putting any breakpoint, that program went to "busy" state in the command window. Why I should put breakpoint in order to make the program run? THX

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Answer by Roger Stafford
on 5 Apr 2014

Edited by Roger Stafford
on 5 Apr 2014

John's function 'powermod' is a very efficient method of solving your problem, but it is possible to solve it in such a way that the solution is eminently clear to you without taking 'powermod' on trust.

To begin with, if you do p = mod(11239388,751), you will know that

11239388 = p + some integral multiple of 751

where p is a certain integer less than 751. Therefore

11239388^375 = (p + that integral multiple of 751)^375

= p^375 + some other larger multiple of 751

by the binomial theorem. Hence the problem is reduced to finding just the quantity mod(p^375,751), which is a lot easier.

You can solve that by starting with 1 and repeatedly multiplying it by p, then taking its mod(~,751), in a for-loop 375 times. Each time the 'mod' operation will keep the number within the necessary upper limit of accuracy for 'double' values before proceeding with the next multiplication. At the end you will have your desired answer.

(Actually in this particular problem you can no doubt arrive at an answer faster than than you could with John's 'powermod' if you only do this last operation 15 instead of 375 times and take a careful look at the answer, remembering that 375 is a multiple of 15.)

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