117 ^ 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......
1this is not that tuff or long.....( it is long)
especially since the power is 256........
1(300)power......will always end with zeroes.....
so
128C0-128C1(11)..............-128C127(11)127(300)+(11)128
1i think easier way will be taking it as ....(300-11)to d power128....
128C0(300)128-128C1(300)127(11)........+128c128(11)128
1I 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
1dude.....sorry to point this out............but a small mistake in ur expansion...........ur second last term must be negative and third last positive..............
117 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
1ya as sky said......findin last digit is enuf i guess...(at this stage).... but i do want a solution for this......
1Well 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?
1U cant follow that method for finding the last 3 digits... that can be done only for the last digit
1dun 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...
1guys ............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.....
1no question is stupid sky................ and also u dint get d answer for it ok??
1Really??? Well It came in RESONANCE AITS last Sunday..... But it isnt a bad question ??? Y do u feel that?/
1http://targetiit.com/iit_jee_forum/posts/last_digit_3209.html
chcek here.
