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If you calculate 3^17,you will get the answer,129140163,and to extract its 2 digits from right,mod it by 100 that is,
number%100.Then you would get the answer 63.

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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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## Comments

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TopNewestLast two digits of a number is the remainder obtained on dividing that number by 100

$3^{17}=3.9^{8}=3.(10-1)^{8}$

In The expansion of $(10-1)^{8}$ all terms are divisible by 100 except two terms which are

$^{8}C_{7}.10.(-1)^{7}+(-1)^{8}=-79$ Remember the 3 which we had separated before, multiply it by - 79 to get - 237

On dividing - 237 by 100 we get the remainder as 63

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Thanks bro!

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Very easy problem bro :P

Hint: Find ${3}^{17} \mod 100$.Log in to reply

Yes i know. But how to compute it?

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Hmm.. answer comes $63$. Is that correct? ( I wasted $2$ pages of my copy to discover that ${ 3 }^{ 15 }\equiv 7 \mod 100$ :P)

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If you calculate 3^17,you will get the answer,129140163,and to extract its 2 digits from right,mod it by 100 that is, number%100.Then you would get the answer 63.

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Suppose it is a big number.Then you can't calculate it..in this case you can

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