FINDING THE REMAINDER USING CONGRUENCES

[@kondowewilas-qe7hp]

To be honest, l have watched several videos on this topic but this one is well explained. Keep this good work high.

[@RexxSchneider]

Where possible, use Fermat's little theorem to reduce the amount of work, especially if you have a large modulo base. a^(p-1) is congruent to 1 mod p where p is prime and a is not divisible by p. So, for example, 2^35 mod 7 can make use of the fact that 2^6 is congruent to 1 mod 7. Therefore 2^35 = 2^6^5 * 2^5 which is congruent to 1^5 x 32 mod 7 which is congruent to 32 mod 7 which is congruent to 4. In the second example you can say that 3^4 is congruent to 1 mod 5 without working through all of the powers to find the one that is congruent to 1. This could save a lot of effort if you're faced with something like 2^100 mod 97.

[@vanilla-vx3pd]

Absolutely aweome, thank you so much for this :)

[@soumya1100]

Many thanks from India

[@goddivine8804]

Kal meri exams hai🤥 these are good for practice

[@abhijitmalik8765]

Thank you so much, I'm from India

[@justinernest2363]

can you give some explanation with regard to equivalence classes. Like what exactly is the background of the manipulation from the bigger number to the smaller number ie 2020 to 4?

[@raginikumari8979]

Helpful

[@rholanangelob.lopena5190]

Sir how did you get the exponent 11 in 7:30

[@sefer-nv6cn]

35 - 2 = 33 33 / 3 = 11

[@sharoncadag9476]

can you explain more how did you got those remainders? thanks

[@thazexperiments5734]

How can do it for when 7^103 is divisible by 25

[@numberexplorerchannel1827]

7^103 mod 25 103 mod 25 = 3 mod 25 Thus, the same as saying 7^3 mod 25 Then, 7^1 mod 25 = 7 mod 25 7^2 mod 25 = 49 mod 25 = 24 mod 25 7^3 mod 25 = 343 mod 25 = 3 mod 25 7^4 mod 25 = 2401 mod 25 = 1 mod 25 7^103 mod 25 = (7^4)^25 * 7^3 mod 25 = (1)^25 * 343 mod 25 = 1 * 343 mod 25 = 343 mod 25 = 3 mod 25 Thus, the remainder is 3. Thanks for commenting

[@henrilaurent1411]

@@numberexplorerchannel1827 hi, could you provide the explanation for the answer because I find 18 as a remainder?...and I am probably wrong but would like the thought process...thank you

[@uyiosemwenkhae8495]

Many thanks to your explanation. Question 1 is a bit complicated as 19^9 gives remainder of 0. None gives remainder of 1 b4 this. So I terminated there. Q1= 0 Q2= 5 my answers

[@tabhinavreddy1725]

superb explanation tq

[@Ranisa12]

How to find remainder 10^50 is divided by 7? Please help

[@Quintessential.96]

How do you get the 114 pls?

[@Spiritual_awakening86]

Remainder when 2016 raise to power 2018 is divided by 11 is.....5

[@brizzxd1793]

Acha

[@sirkeitv05]

well explained Sir 💪❤️👏 thanks for this video hope you would take some more helpful videos regarding Number Theory sub ❤️

[@mariefedeguzman440]

How can i get the remainder when 2²⁰⁰ is divided by 5

[@ivayloivanov5766]

Can you help me with this, please: x ≡ 2 (mod 11) x ≡ 9 (mod 15) x ≡ 7 (mod 9) x ≡ 5 (mod 7) ?

[@golloramesh1637]

I honestly won't understand🙏

[@sanjaysurya6840]

Mathematics is the father of ______. Fill in the blank 👨‍🏫

[@tengisjargal6986]

1) answer 1 2) answer 5

[@cheche5517]

What is the given in no.2 TRY THESE?

[@pksingh3126]

The answer, Q.1) 01 Q.2) Trying..

[@rajwantkaur2158]

I'm getting remainder 3 when I'm diving 4 by 15. Please help me out.

[@tebogomodingoane3967]

me too

[@tebogomodingoane3967]

did you get a solution

[@michaelwilliams986]

You’re dividing 15 by 4 not 4 by 15

[@maitreyo_das]

If you divide 15 by 4 then obviously remainder is 3 but 4/15 gives 4 (explanation-> 17/15 gives you remainder 2 coz 17= 15x1 + 2, 33/15 gives remainder 3 coz 33= 15x2 + 3, similarly 4/15 gives remainder 4 coz 4=15x0 +4)

[@rajwantkaur2158]

@@maitreyo_das Thanku

[@vincentrinon96]

I wont understand,😭😭

[@jaysonbarbero1547]

😴 sorry Sir absent ako that day😂✌️

[@jaysonbarbero1547]

Hug Sir