another remainder pbm.........

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shaheen12342's picture
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What is the remainder when (17)^36 + (19)^36 is divided by 111

atul duggal's picture
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2shaheen

is the answer is 2

shaheen12342's picture
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hi atul, even i m gettin

hi atul,
even i m gettin d ans as 2.i applied chinese thm...wht is ur approach? i ll let u knw d ans as soon as i come to knw abt it...

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Solution

Lets see that 3x37 =111 in the denominator

and Consider the first term 17^36 then 17^37/17 adding and subtracting 1 we get 17^37/17 -1 + 1 where in the first two term become (17^37 - 17)/17 + 1 first term is divisble by 37 and remainder is 0 and second gives remainder as 1 similarly for the other terms also we get 1 as remainder. Total remainder is 1+1 =2

atul duggal's picture
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@ahaheen

hey buddy i solve it using euler...

atul duggal's picture
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@mssansanwal

hey buddy m not getting ur sol..can u pls explain it further

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explain euler theoram

can u explain how to solve this ques wid euler theoram???

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deepikia (not verified)
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Remainder of (17)^36 +
Remainder of (17)^36 + (19)^36 divided by 111
= Remainder of (17)^36 divided by 111 + Remainder of (19)^36 divided by 111
    __________p1________________             __________p2___________________
 
p1 = Remainder of (17)^36 divided by 111
 
111 = 3 x 37
and Both are co-prime to each other
 
Remainder of (17)^36 divided by 3
= Remainder of (-1)^36 divided by 3
= 1
 
Remainder of (17)^36 divided by 37
Euler number of 37 = 36,
Remainder of (17)^36 divided by 37 = 1 [ Fermat’s little theorem can also be used : ap−1= 1 (mod p). ]
 
So p1 = 1
 
Proceed similarly and u ‘ll get p2= 1

Thus the answer =2

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plz explain or give link

plz explain or give link...............of how to find euler number..............

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@ Nilay
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Hello, introduction

Hey. New here and figured I should post and say hi.

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