Mathematical Induction with Divisibility: 3^(2n + 1) + 2^(n + 2) is Divisible by 7

In this video I prove by induction that 3^(2n + 1) + 2^(n + 2) is divisible by 7 for all nonnegative integers n. I hope this video helps:)

[@juandirection3751]

Hands down the most clear explanation of divisibility induction I've seen. Genuinely thank you and congratulations every single video of yours on induction I've seen holds up as well

[@TheMathSorcerer]

thank you!

[@zacharyjohn329]

Wow I had been stuck on a problem for literally hours. This was the best explanation ive seen. Thank you

[@extramiletvesonucc.2892]

You are indeed a Maths sorcerer. I've tried proving this particular question but it seemed almost impossible till I watched this and saw my mistakes. Thanks a lot.

[@johubify]

THANK YOU SIR! YOU ARE SO KIND SIR, YOU ARE SUCH A BIG MATHEMATICIAN, BUT ALWAYS SO HUMBLE, THANK YOU! :):):)

[@TheMathSorcerer]

Thank you!!

[@aldoumene6201]

Best explanation ive seen so far ! Thank you 🙏

[@MdFaizan-th5yf]

Jeff Bezos before Amazon (without haircut)

[@saumytiwari7]

Thankyou so much.. Tomorrow is my exam and u helped me a lot.. Idk the result.. But u gained so much respect

[@TheMathSorcerer]

Good luck!

[@louissilsby8819]

I have been looking for so long for this exact kind of question, i messed this up in my exams. Thanks a bunch.

[@konchu5221]

was struggling on precalc review... thank you this helped so much

[@leviackerman3033]

Was doing a pastpaper and it had this question, i was so frustrated because i couldn't get the answer and I'd been trying for hours.... until i found this!. You're literally an angel, Thankyou for this! Your method is way easier...the f(k+1) -f(k) got me confused but now i get it

[@leanneteh8307]

tq for nailing things out, got so much clearer now

[@TheMathSorcerer]

Excellent!

[@fleurysankara5081]

respect to you sir you always make things clear all the way from Africa

[@TheMathSorcerer]

wow that's awesome, Africa so cool! Very happy it helped!!

[@GouravSharma-tb6zh]

Samina mina ay ay ।

[@bgaming93]

You helped me a lot sir, for my exam. 💕 from India :)

[@alokmandal6353]

Great way of understanding the concept .. Love from India

[@tareq5264]

thank you man, you are a genius

[@Thabang_Kgatla1]

Would I be correct if I said that the value of m on the formula b =ma is the base case?

[@user-fq1bo1lb5w]

Amazing!

[@LakshayDhaka08]

Excellent sir (from India)

[@jacknyirenda7237]

This helped. Thank you.

[@user-tx5hc2rp2c]

what if instead it was a greater than or equal to sign instead of a plus sign? Ive been having problems finding examples where the lhs and rhs are both to the power of K

[@blalalalahd194]

what does claim mean mathematically saying sir, i often heard that word whenever i see someone proving their argument in math also the other words like trivial etc where all of that words came from sir

[@admiremutero9036]

You a great teacher. Thank you sir

[@TheMathSorcerer]

You are welcome!

[@sergeigrigorev2180]

Here is how to proof 3^(2n + 1) + 2^(n+2) is divisible by 7 w/o induction. 3^(2n+1) + 2^(n+2) = 3*9^n + 4*2^n = 3*(2+7)^n + 4*2^n = 3*2^n + 4*2^n (mod 7) = 7*2^n (mod 7) = 0 (mod 7). Therefore 3^(2n+1) + 2^(n+2) is divisible by 7.

[@realndu]

Legend!!

[@enayahkhan6491]

Respect to you sir ......u are great helper ..I'm from Pakistan

[@TheMathSorcerer]

Thank you !

[@leviackerman3033]

The "2 blah + 7 blah is 9 blah" had me rolling.

[@SkylanderBlazier]

Wow this was so helpful!

[@TheMathSorcerer]

👍

[@neilbhavikatti6720]

Thanks so much!!!

[@TheMathSorcerer]

You are welcome!

[@kimberleysinclair7140]

Thank you, great explanation

[@TheMathSorcerer]

You are welcome!

[@davidfisher9626]

you deserve the title math sorcerer

[@sebalizarraga1051]

awesomeee

[@mo7.998]

if i got 7(9m+2^k+2) as a proof is it ok ? or it just has one solution ?

[@ELLIPTICALWR]

how would you use proof by induction to prove a function is not divisible by a real number, like n^3 +2 for example is not divisible by 8

[@tariromakombe7914]

Brilliant

[@ultragamer4465]

GIGACHAD THANK YOU MY BROTHER

[@freakx198]

amazing

[@nifahadjiabobakar6402]

How about for all positive integers n?

[@littlethphuong1840]

thank you

[@alexreynolds9710]

thank you the math sorcerer!

[@omeedmehrzad6089]

thank you Alex Reynolds!

[@alexreynolds9710]

@@omeedmehrzad6089 Thank you Kate Mehrzad!

[@jemanvirk]

Thanks sir

[@markdave2456]

When you first learned proof by induction, did it feel like circular reasoning to you?

[@TheMathSorcerer]

I actually did not even understand the reasoning behind it. I could write the proofs but didn't understand why induction worked. I remember reading my book over and over. It kept talking about dominoes and I didn't understand. I was able to prove things with it though. The only proofs I really struggled with were the inequality ones, soooo hard for beginners!!

[@TheMathSorcerer]

So yes, it felt circular I think. I just remember not understanding why it worked, at all!! I should make a video on that, explaining why it actually works intuitively and mathematically.

[@johubify]

@@TheMathSorcerer yes sir, that would be perfect! I am able to prove using the Induction method, but the problem is, that I do not feel it is rigorous, and I do not understand that why does it always seem to work for k+1

[@johubify]

Mark Dave Yes buddy!

[@ahmedlutfi4894]

beautiful

[@aniketvasu1722]

Thanks Man

[@chessandmathguy]

2:23 did you mean "when n equals k plus one" and not "k plus two?"

[@cpw1769]

Thx

[@betul1445]

What is mean 7m i did not got it

[@sakshu6549]

👍

[@tymzon7446]

i love you

[@ianmi4i727]

Calculus I !!! :)

[@TheMathSorcerer]

😀

[@farhanfarooq9074]

love from Pakistan

[@TheMathSorcerer]

❤️

[@franzsenkelo6246]

Bad teaching

[@uscybercom6009]

Thx Bro👍

[@siggimatti1129]

Hey I have a similar problem 7 | 3⌃(4n+1)-5⌃(2n-1). So I end up with way bigger numbers going through the problem, 81 and 25 if you test the problem you'll see what I mean, I don't really know what to do with them, any help would be appreciated!

[@siggimatti1129]

to further explain he gets 9 and 2 but I get 81 and 25 so it's a bit more complicated

[@sasukeutchiwa3600]

Tnx sir