1317256 = (20-3)256
last 3 digits of 17256 = last 3 digits of 256C254.202.3254 - 256C255.20.3255 + 256C256.3256
= 256C2.202.3254 - 256C1.20.3255 + 256C0.3256
hope u can solve it now...
12 Answers
1313All the other digits of d expansion of (20-3)256 will have last 3 digits as 0 ... hence finding d last 3 digits of above expression gives d answer...
1Continuation after MAK'S explanation
=3254 ( 256 C 2* 202 - 256 C 1* 20*3 + 256 C 0 32)
= 3254 * 13040631
NOW THE PROBLEM IS YOURS
SOLVE 3 254 AND FIND THE ANSWER
1im getting 681
and im sure thats the answer only the method was a bit dirty and bad so i wouldn't post it
maybe someone else can give some enlightening or short method
4If Harry Potter's Calculation is correct then i think last 2 digits shud be 79
(as 3 254 ends in 9)
623254 = 9127 = (10-1)127
(this is multiple of 100) + 127C126x10x(-1)126 + 127C127x(-1)127
= 1270 - 1
so i am getting the last 2 digits as 69
1@ nishant bhaiyya : i checked it with a calc just now and it does not give 69 as the last two digits...
maybe its because of some overflow...
it was such a long time back, i think i did this using congruencies ... lost it completely by now
1By congruency ,
17256 = 289128
but 289 = 11 (mod 100)
so 17256 = 11128(mod 100)
again 11φ(p) = 1(mod 100)
φ(p)=100 ( 1-1/2 ) ( 1-1/5 ) = 40
so 1140 = 1(mod 100)
so 11120 = 1(mod 100)
again 11128 = 118(mod 100)
but 112 = 21(mod 100)
so 118 = 214(mod 100)
but 212 =41(mod 100)
so 214 = 412(mod 100)
so basically , it comes down to this-------------
17256 = 412(mod 100)
= 1681 (mod 100)
so last 3 digits --- 6 8 1
hope you liked my way , because i didn't use any calculations invoving higher powers other than 2 which cannot be done without using calculators ,otherwise the ans. would be there at the eight -th step only ----------------at least Nishant sir please reply
21ans is 681 but i din get wat u did sawmya.....further if u hav to find last three digits of a number than u hav to find the remainder when 17256is divided by 1000 rather than 100 and further if remainder is 681 than it shud be
17256≡681 mod 1000 rather than 17^256 = 1681(mod 100)
remainder cant be greater than divisor
