Monday, February 6, 2017

elementary number theory - Find the last two digits of $2^{2156789}$

Find the last two digits of $2^{2156789}$.



My try:




As $2156789 = 4* 539197 + 1$
The unit digit of $2^{2156789}$ is similar to the unit digit of $2^{4n+1}$ which is equal to 2.
But I'm unable to find the tens digit. Please help me.

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