Negative Remainder and Chinese Remainder

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Solution for Practice Question:
Solution 1:
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Solution 2:
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Solution 3:
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Solution 4:
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[@kavitajoshi4132]

on dividing a number by 4,5,6 we get 3,4,5 as remainder .find the least number for this question how can we apply this approach here

[@udaypaluri]

How to do that problem 6 when options aren't given? I have opted Euler's number method but it is getting cumbersome. Any other approach @Bullseye?

[@academichead-quanthitbulls7991]

Euler no. is 96. You divide the power and you are left with 13^5/360. This you can write as (13^2)* (13^3)/360. Solve these two you get 169*37/360. Which you can multiply, divide and get the remainder as 133. Thus it can answered like this as well.

[@pranavmore2697]

sir how you got 37 in 13^3/360 ?

[@hitbullseye]

13^3 is 2197. Divide 2197 by 360 and you get the remainder as 37.

[@svkguha]

What was the remainder when India was divided by Nehru and Jinnah?

[@MsRyanstone]

Bangladesh

[@srbh711319]

And quotient was pakistan. That means India= pakistan*k + bangladesh. Now what is K here?

[@ichamatitales9459]

If I would have been a Pakistani I would comment K‹1

[@Mdp3118]

finding remainder with euler noconcept is very helpful,,but what about the case when 15^43/121 ...help

[@academichead-quanthitbulls7991]

Then you have to apply remainder cyclicity. But do remember it is not possible to find the remainder for each and every question. Sometimes the time a question make take to be answered, it is better to leave and move ahead. Here only cyclicity will have. But it can go as long as 43 steps i.e. the power of the numerator given.

[@riddhibhalla5196]

unable to understand the solution of Q6. would you please explain again?

[@hitbullseye]

photos.app.goo.gl/VgfQGHzM3a2Wza2p2

[@gautamkumar007]

if 7/4.. remainder is 3... but u will take -1 as remainder... plz explain whats wrong in 3...? plz

[@academichead-quanthitbulls7991]

Nothing is wrong with 3. Just go through the other comment given. You will understand, where you should follow what approach.

[@ninderchitosiya5326]

14^98/25=? ka remainder kya hoga explain krna plz

[@academichead-quanthitbulls7991]

You need to make cyclicity for this. The remainder you obtain, when 14^1, divided by 25 is 14 only and then for the next four powers it comes out to be 21, 19, 16 and 24 respectively. Now a remainder of 24 can be taken as -1. The question can be thought as (14^95)*(14^3). From this the remainders are - 1 and 19. The product becomes - 19. Hence the final answer to the question would be 25 - 19 = 6.

[@ninderchitosiya5326]

Sr chanig remainder theorem or Euler's Theorm dono me se kha or kab konsi use kre plz tell me

[@gautamkumar007]

in the whole video u never explain , why and when we should take negative remainder .. u took some where randemoly negative remainder some where not ... ?

[@academichead-quanthitbulls7991]

The negative remainder should be ideally only taken in case the numerator is 1 more or 1 less than any multiple of the denominator. Bcz 1 is the only number whose any power ends in 1 or - 1. No other number has that property. Otherwise for the questions where there is no power attached to the numerator, you can take it if you feel taking negative remainder reduces your calculations.

[@spareyourbrain]

why are you keep reminding the word "student"?

[@kayenatrahmat5689]

Solution for practice question 1 should be 25. Correct me if I'm wrong

[@academichead-quanthitbulls7991]

Solution for practice question 1. photos.google.com/share/AF1QipMFMWl74fhj0_tmVR-U1WdqD3df5DdX57snb-P8ijBDHAN_11EUMRF3lPdSlRBhzA?key=MC1HR0pWNTB2aWdLNC14YV9Id18takczTEJ4UXpB