IIT JEE , AIEEE Forum - Mathematics , Algebra

sandeepramesh

Let me say that im guilty of posting too easy a problem so ill post another Mr. Green

This one's decent Mr. Green

Show that if m ends with the digit 5, then $1991 | 12^m + 9^m + 8^m + 6^m$ Smile

pottermania1990

wat do u have to prove?

sandeepramesh

$1991 | 12^m + 9^m + 8^m + 6^m$ ?? Cant you see that

Note the notation a|b means a divides b so you have to prove that 1991 divides that expr

vikas_k

hey heard dat ders sum question wrong in IPE chemistry paper(2nd year)....is dat true??

sandeepramesh

man why do you spam here???

EDIT: Noticed that u are new to this forum, plz post in the relevant place :)

pottermania1990

u can write the given expression as

(3^m + 2^m)*(3^m + 4^m)

m = 5k given in qn..

(3^5k + 2^5k )*(3^5k + 4^5k )

for k =1

we get 275*1267/1991 = 175
since it is true for k= 1

by induction we can say that it is true for all k in N

sandeepramesh

yeah that's a plausible method :)

But induction isnt always the shortest and the most elegant method :)

Note: this isnt undermining ur answer in any way, just that there exists more solns :)

pottermania1990

is it rite?

sandeepramesh

think so :)

arpan1

rate me first dude to get the solution (o-called elegant)

sandeepramesh

I FORGOT TO SAY! THANX ARPAN!

THAT NO PERSON WHOMSOEVER WILL BE ENCOURAGED IN ALL MY POSTS IF THEY BEG FOR RATES AS IF ------ (CENSORED :D)

computer001

oh hello arpan u rosy lad..u shud use tht as ur signature u no "rate me n il post the solution

"

arpan1

@sandeep

it doesnot matter to me if u rate or not..

i hope u know the solution

however ifu want a decent solution beter rate me than find people to get it done as if ******

anandghegde

if you have come here for rates, then

http://www.goiit.com/posts/list/15/about-non-iits-how-to-cheat-goiit-for-rates-and-altitude-48069.htm

Sushmi

Are these problems for IIT JEE or any other competitives? I guess not.

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