You can put this solution on YOUR website! find by mod (100) the last two number of
2^100
= 2^(10^2)
= [2^10]^2
= [1024]^2
= 24^2 (mod 100)
= 576 (mod 100)
= 76 (mod 100)
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and
2^2006
2^100 = 76 (mod 100)
2^200 = 5776 = 76 (mod 100)
2^400 = 5776 (mod100) = 76 (mod 100)
2^800 = 2^1600 = 76 (mod 100)
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2^2006 = 2^1600*2^400*2^6 = 76*76*64 (mod 100)
= 76*64 mod 100
= 4864 mod 100
= 64 mod 100
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Cheers,
Stan H.
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