Is there any shortcut way to find the last two decimal digits of a modular exponentiation (base always is a single digit number) without doing square and multiply?
As an example in $$2^{100001} \pmod{10001}$$
the last two decimal digits are 48.
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So, what, you're taking the modulus twice? First mod 10001, then mod 100? – Mike Apr 22 '13 at 07:49
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@Mike,Yes, I want the last two digits of the first modular operation so it requires another (mod 100) on the result of the first mod. – Mohsen Afshin Apr 22 '13 at 07:53