Last 3 digits

find the last 3 digits of 17to the power 256.

25 Answers

1
Akand ·

can we convert into 1728.............and do sumthing about it???

1
Anuj ·

why dont try taking log?????it will simplify things a lot.........

11
Mani Pal Singh ·

how?????????

39
Dr.House ·

caculations may become cumbersome but congruencies can help.

1
Philip Calvert ·

17 ^ 2 leaves 289

17 ^ 4 leaves 521

17 ^ 8 --- 441

17 ^ 16 -- - 481

17 ^ 32 ---- 361

17 ^ 64 -- 321

17 ^ 128 ------ 41

17 ^ 256 ---- 681

im sorry but it was really long and boring two digits would have been much better.........but three is a waste.......
anyway thats the answer......

1
Philip Calvert ·

this is not that tuff or long.....( it is long)
especially since the power is 256........

1
Akand ·

(300)power......will always end with zeroes.....
so
128C0-128C1(11)..............-128C127(11)127(300)+(11)128

1
kamalendu ghosh ·

Yes it is.... calculations a bit easies thanxxx

1
Akand ·

i think easier way will be taking it as ....(300-11)to d power128....
128C0(300)128-128C1(300)127(11)........+128c128(11)128

1
kamalendu ghosh ·

I hope u got it?

Sorry if i have wasted ur time if u think it a nit-so-worthy at this point of time sum

1
kamalendu ghosh ·

sorry for that...

1
Akand ·

dude.....sorry to point this out............but a small mistake in ur expansion...........ur second last term must be negative and third last positive..............

1
kamalendu ghosh ·

17 to the powr 256 = (172) to the power 128
= (290 - 1)to the power 128

= .... .... ... ... ..- 128C125(2903) + 128C126(2902) - 128C127(290) + 1(290) + 1
= 1000k - 128C126(2902) - 128C127(290) + 1(290) + 1

Now calcul;ate bit to get 681 as the answer

1
Akand ·

wel last digit is 1.............must think bout d oder 2

1
KR ·

i think we will get if we use modulo

1
Akand ·

ya as sky said......findin last digit is enuf i guess...(at this stage).... but i do want a solution for this......

1
kamalendu ghosh ·

Well sky, I can find the last 5 digitd but it wud need a bit big multiplications.....

well, were u avle to solve it or not?

1
kamalendu ghosh ·

U cant follow that method for finding the last 3 digits... that can be done only for the last digit

1
skygirl ·

dun bash me this way guys.... am sry to say it in dat way if it did hurt u all...

but if i ask u abt the 5th last digit... how will u find it ...

well nishant bhiaya told its a 'wat to say' ... not worth-doing question r8 now...

sry once agn...

1
Akand ·

guys ............for d first few multiples i got d second digits as......(i used a calculator though)..1 8 1 2 5 6 7 4.........no specific trend.....

1
Akand ·

no question is stupid sky................ and also u dint get d answer for it ok??

1
kamalendu ghosh ·

Think akand ... think...

1
kamalendu ghosh ·

Really??? Well It came in RESONANCE AITS last Sunday..... But it isnt a bad question ??? Y do u feel that?/

1
skygirl ·

http://targetiit.com/iit_jee_forum/posts/last_digit_3209.html

chcek here.

1
skygirl ·

hey this is a bad question.... i asked this few days ago....

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