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Algebra

New kid on the Block

 Joined: 26 Dec 2007 Post: 1
26 Dec 2007 10:46:02 IST
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8
708
when 43 raise to power 43 is divided by 37 ,what is the reminder?
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

when 43 raise to power 43 is divided by 37 ,what is the reminder?

Blazing goIITian

Joined: 18 Feb 2007
Posts: 1042
26 Dec 2007 10:55:15 IST
1 people liked this

write 43^43
as
(37 + 6)^43

now expand binomially

the remainder will come only from the last term 43C43 643

New kid on the Block

Joined: 11 Jul 2007
Posts: 15
26 Dec 2007 11:14:47 IST
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Priyesh is rite..........i go by his answer.........

Blazing goIITian

Joined: 27 Nov 2007
Posts: 470
26 Dec 2007 11:17:42 IST
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Blazing goIITian

Joined: 13 Aug 2007
Posts: 687
26 Dec 2007 14:08:04 IST
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priyesh sabse bada 'gadha' hai aur jo use support kar rahein hain woh bhi

bhaisaab 6^43 ko further 37 se divide nahi kar sakte kya. foolish people

Cool goIITian

Joined: 21 Dec 2007
Posts: 33
26 Dec 2007 14:11:58 IST
1 people liked this

6^43=36^21*6= (37-1)^21*6 =37k-6 so the remainder is 31 ....

Blazing goIITian

Joined: 18 Feb 2007
Posts: 1042
26 Dec 2007 14:37:26 IST
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hey sree
who said we can't divide it further i have just said that the remainder will arise from the last term.rest division can be done by the author himself.

i have nowwhere written that answer is the last term obviously remainder wil be less than 37

also do mind ur language

Blazing goIITian

Joined: 13 Aug 2007
Posts: 687
26 Dec 2007 19:01:19 IST
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Yaar srry for that rough stuff.

i was in tension so i wrote that. purpose was nt to hurt u yaar . i am really srrry

i promise this will nt be repeated in future

if u are satisfied that u can nudge me.

bye

Scorching goIITian

Joined: 5 Dec 2006
Posts: 225
26 Dec 2007 20:07:19 IST
1 people liked this

write 643 as 6(36)21

=6(37-1)21 = expanding it binomially we get

37i - 6 where i is an integer

=37i-6+37-37
=37i+31
hence remainder should be 31

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