Mathematical induction (1 Viewer)

[AfroNerd]

Okay guys, so I'm making this new thread for anyone who wants to practice induction.

 

[AfroNerd]

We'll start off with some of these

 

[porcupinetree]

Note: don't actually attempt this question

 

[wu345]

Prove n^5-n is divisible by 30 for all natural numbers

 

[leehuan]

Prove n^5-n is divisible by 30 for all natural numbers

Is this one similar to the proof for n⁷-n|42?

 

[Paradoxica]

Is this one similar to the proof for n⁷-n|42?

Faster alternatives:
Fermat's Little Theorem
Basic facts about arbitrary runs of consecutive integers
Brute Modular Force

 

[leehuan]

Faster alternatives:
Fermat's Little Theorem
Basic facts about arbitrary runs of consecutive integers
Brute Modular Force

Isn't that the same way you prove n⁷-n|42?

 

[Paradoxica]

Isn't that the same way you prove n⁷-n|42?

Prove (n(n-1)/2)|(n^k-n)
for all k in N

Yes, the proof is identical.

 

[AfroNerd]

How would u do question 2, 3 and 4 I couldn't do step 3 on them