Using Mathematical Induction to Prove 2^(3n) - 3^n is divisible by 5

In this video, we prove that the expression 2^(3n) - 3^n is divisible by 5 for all positive integers of n, using mathematical induction.

The first step is to use the basis test to show that this condition holds true for n = 1.

Then we can show that this can be expressed as any multiple of 5 through the inductive test.

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[AthenianStranger]

This was immensely helpful. After failing to understand proofs for 14 years I finally did one and understood it. Thank you. You earned a like and a subscriber.

[ROKZILLA]

Very helpful. Finally solved my maths paper’s final problem: Prove 4^n +15n - 1 is divisible by 9

[crackboyumar]

I’m a mathematics student, and this is so useful. Thanks

[marilynortiz]

YESS thank you so much! I was having trouble with this problem! You are truly the Master!!

[simoncianci]

Absolutely useful. Thanks a lot, I was having a hard time finding an example of how to think the induction when n is used as an exponent

[osmanreyes]

Thank you! Your explanation is very clear. I didn't get proof by induction before watching your video!!!! It helped me a lot.

[pangolinkazoo]

I've got my FP1 exam tomorrow and this was really helpful. Thanks man

[melusinyoni]

Thank you Sir, this is the most clearly explained P.M.I I wish I could get the same on permutations

[westronic]

Thank you!! I used this strategy to prove 5^(2n) - 2^(5n) is divisible by 7 for all natural n.

[saran]

This helped greatly! You should do more videos since you explain complex proofs so well.

[jjjggg]

Thank you very much. I really didn't know that.

[wiggles]

For some reason, youtube keeps recommending videos like this to me. I keep saying that modular arithmetic solves them almost immediately, as is the case here. 2^(3n) - 3^n = (2^3)^n - 3^n = 8^n - 3^n = 3^n - 3^n = 0 mod 5, and induction didn't even need to be used, it was a direct manipulation of the expression.

[kishanpoddar]

Thank yo so much for this video Sir !
(10^2n-1+ 1 is divisible by 11) please can u do a video on this problem as well ?

[haris]

Seriously man, ur video was very helpful

[nk_r]

only your video can make me understand this 😂 . thank you soooo much!!

[pumlanimamsundu]

Was i the only one who forgot what was done at 8:40 ?

Thanks a lot man

[tinkageorgewilliam]

prove that if x and y are natural numbers such that k=(x^2 +y^2)/xy is an integer, then k=2

[DMann-xjmg]

Could you show a proof using mathematical induction of n^3 - n is divisible by 3 for all n> >=2?

[ritesha]

thanks, i was doing my tutorial, i wrote equations for case n=k and n=k+1, then i was like now whattt do i do😂

[ruthzkycanz]

How about 8|5^n-1 +2(3)^n-2 +1 .? How to prove it