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Asked: 2026-06-07T03:22:33+00:00

I want to code for calculating the value of pow(a,b)%MOD. I use C++ to

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I want to code for calculating the value of pow(a,b)%MOD. I use C++ to code.

But the problem is the value of b can be very large. I know the log(b) time complexity method. But, the value of b might not fit in the data type “long long” of C++. For example b can be 1000000000 th Fibonacci number. Exact calculation of such a big number is itself, not possible (in time limits).

P.S. :

  • pow(a,b) means a*a*a*a*… b times.
  • X % MOD means the remainder obtained on dividing X by MOD.
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1 Answer

  1. Editorial Team

    That’s a typical task. Please (or, really, PLEASE!) read about the Euler’s totient function.

    And then the Euler’s theorem.

    The thing is you can dramatically reduce a^b to a^(b % phi(MOD)). Yes, you will need some kind of an integer factorization method, but still, no crazy ideas about actually calculating the power needed.

    We did such samples by hand in my youth 🙂 Even when the numbers where far beyond 32/64 bit range.

    EDIT: Well, you live and learn. In 2008 the result is obtained:

    “The totient is the discrete Fourier transform of the gcd: (Schramm (2008))”

    So to calculate phi(b) one does not need to know its factors.

    EDIT(2):

    And the Carmichael’s function is what you need to calculate to get the correct answer for any a, b and MOD.

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