Question

How can I prove $1^{n+2} + 2^{n+2} + 3^{n+2} + 4^{n+2}$ is divisible by $10$ for any odd $n$?

score 91 · Answer 1 · 2026-04-04 13:33:03

91

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How can I prove $1^{n+2} + 2^{n+2} + 3^{n+2} + 4^{n+2}$ is divisible by $10$ for any odd $n$?

Published on 04 Apr 2026 - 13:33

score 405 · Answer 2 · 2016-07-17 22:29:33

405

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Proving $ \bigcup_{i=1}^n A_{i} \text{ is finite.} $ by Induction.

Published on 17 Jul 2016 - 22:29

score 609 · Answer 3 · 2026-04-11 20:46:45

609

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Clarification on inductive proof of Bernoulli's inequality

Published on 11 Apr 2026 - 20:46

score 4.9k · Answer 4 · 2016-07-18 19:54:40

Prove that if a collection of subsets of {1,..,n} that each pair of subsets has at least one element in common, there are at most $2^{n-1}$ subsets

score 63 · Answer 5 · 2016-07-19 09:19:07

Prove that $\sum_{i=1}^{n^2} \left \lfloor \sqrt{i} \right \rfloor = \frac{n(4n^2 - 3n + 5)}{6} $ using induction?

score 84 · Answer 6 · 2016-07-21 17:20:37

84

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How do I prove that for $\forall n\in \mathbb{N}$ $\sum_{k=1}^{n}k(k+1)=\frac{1}{3}n(n+1)(n+2)$?

Published on 21 Jul 2016 - 17:20

score 823 · Answer 7 · 2026-04-12 04:01:52

823

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How to prove by induction that $3^{3n}+1$ is divisible by $3^n+1$ for $(n=1,2,...)$

Published on 12 Apr 2026 - 4:01

score 205 · Answer 8 · 2016-07-21 19:59:49

205

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Prove by induction that $a^{4n+1}-a$ is divisible by 30 for any a and $n\ge1$

Published on 21 Jul 2016 - 19:59

score 341 · Answer 9 · 2026-04-12 07:19:30

341

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CLRS substitution method "subtracting constant" technique

Published on 12 Apr 2026 - 7:19

score 161 · Answer 10 · 2026-04-03 18:47:34

161

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Induction Method in a special case of $ n!+1 = m^2 $ (Brocard's Problem)

Published on 03 Apr 2026 - 18:47

score 304 · Answer 11 · 2026-04-12 01:44:40

304

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Proof related to Harmonic Progression

Published on 12 Apr 2026 - 1:44

score 112 · Answer 12 · 2026-04-10 11:48:38

112

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Need help with inductive proof of Binomial Theorem

Published on 10 Apr 2026 - 11:48

score 281 · Answer 13 · 2026-04-11 15:00:50

281

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Mathematical Induction Inequality problem

Published on 11 Apr 2026 - 15:00

score 543 · Answer 14 · 2016-07-23 17:32:21

543

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How to prove if this $\sum_{l=0}^{n}\binom{n}{l}=2^{n}$ is valid for all $n\in \mathbb{N}$?

Published on 23 Jul 2016 - 17:32

score 255 · Answer 15 · 2026-04-11 01:02:04

255

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Difference between set theory proof and logic proof of complete induction

Published on 11 Apr 2026 - 1:02

List Question

How can I prove $1^{n+2} + 2^{n+2} + 3^{n+2} + 4^{n+2}$ is divisible by $10$ for any odd $n$?

Proving $ \bigcup_{i=1}^n A_{i} \text{ is finite.} $ by Induction.

Clarification on inductive proof of Bernoulli's inequality

Prove that if a collection of subsets of {1,..,n} that each pair of subsets has at least one element in common, there are at most $2^{n-1}$ subsets

Prove that $\sum_{i=1}^{n^2} \left \lfloor \sqrt{i} \right \rfloor = \frac{n(4n^2 - 3n + 5)}{6} $ using induction?

How do I prove that for $\forall n\in \mathbb{N}$ $\sum_{k=1}^{n}k(k+1)=\frac{1}{3}n(n+1)(n+2)$?

How to prove by induction that $3^{3n}+1$ is divisible by $3^n+1$ for $(n=1,2,...)$

Prove by induction that $a^{4n+1}-a$ is divisible by 30 for any a and $n\ge1$

CLRS substitution method "subtracting constant" technique

Induction Method in a special case of $ n!+1 = m^2 $ (Brocard's Problem)

Proof related to Harmonic Progression

Need help with inductive proof of Binomial Theorem

Mathematical Induction Inequality problem

How to prove if this $\sum_{l=0}^{n}\binom{n}{l}=2^{n}$ is valid for all $n\in \mathbb{N}$?

Difference between set theory proof and logic proof of complete induction

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