Question

For all $a,b,n \in \mathbb N$, $0 \leq n(a+b+1)-n^2 +b$

score 41 · Answer 1 · 2026-03-28 09:28:03

41

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For all $a,b,n \in \mathbb N$, $0 \leq n(a+b+1)-n^2 +b$

Published on 28 Mar 2026 - 9:28

score 87 · Answer 2 · 2026-04-10 18:50:35

87

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How prove the finite induction

Published on 10 Apr 2026 - 18:50

score 92 · Answer 3 · 2026-03-29 04:26:19

92

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Prove that $f_{2k} \cdot f_{(2k+4)} + 1$ is a perfect square, where $f_n$ is the $n$th Fibonacci number, $n\geq0$.

Published on 29 Mar 2026 - 4:26

score 66 · Answer 4 · 2020-06-25 07:40:33

66

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$S$ a set of positive integers, all subset sums distinct. Does it hold that $\max S\ge 2^{|S|-1}$? Generalized.

Published on 25 Jun 2020 - 7:40

score 500 · Answer 5 · 2026-03-27 16:09:17

500

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Cauchy Product of $m$ series

Published on 27 Mar 2026 - 16:09

score 79 · Answer 6 · 2026-03-30 10:56:46

79

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Show that these elements are linearly independent

Published on 30 Mar 2026 - 10:56

score 147 · Answer 7 · 2020-06-27 19:04:57

147

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Proof checking : if $A$ and $B$ are finite sets then so $A \cap B$ finite

Published on 27 Jun 2020 - 19:04

score 532 · Answer 8 · 2026-04-11 09:45:40

532

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Can you solve any induction problem with base case 0

Published on 11 Apr 2026 - 9:45

score 222 · Answer 9 · 2026-04-03 12:12:04

222

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Can this inductive proof that $\sum_{i=0}^n2^{2i+1}=\frac23(4^n-1)$ be simplified?

Published on 03 Apr 2026 - 12:12

score 97 · Answer 10 · 2020-06-29 15:11:46

97

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Prove $(1 + 1/n)^n \le n+1$

Published on 29 Jun 2020 - 15:11

score 40 · Answer 11 · 2026-04-03 15:59:18

40

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If $\frac{a}{k} - \frac{a(c-1)}{kb} > 1$, is $\frac{a}{k+1} - \frac{a(c-1)}{(k+1)b} > 1$?

Published on 03 Apr 2026 - 15:59

score 47 · Answer 12 · 2020-06-30 02:11:18

47

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Sum of all subsets of the set of even coprime integers relative to a power of a prime

Published on 30 Jun 2020 - 2:11

score 81 · Answer 13 · 2026-04-09 07:24:24

81

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Proving binomial sum using mathematical induction

Published on 09 Apr 2026 - 7:24

score 146 · Answer 14 · 2026-04-10 22:40:40

146

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Prove by mathematical induction, that $81\times 3^{2n} - 2^{2n}$ is divisible by $5$ where $n \in \mathbb{Z}^+$

Published on 10 Apr 2026 - 22:40

score 98 · Answer 15 · 2026-04-12 00:40:54

98

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Proof with binomial coefficients and induction

Published on 12 Apr 2026 - 0:40

List Question

For all $a,b,n \in \mathbb N$, $0 \leq n(a+b+1)-n^2 +b$

How prove the finite induction

Prove that $f_{2k} \cdot f_{(2k+4)} + 1$ is a perfect square, where $f_n$ is the $n$th Fibonacci number, $n\geq0$.

$S$ a set of positive integers, all subset sums distinct. Does it hold that $\max S\ge 2^{|S|-1}$? Generalized.

Cauchy Product of $m$ series

Show that these elements are linearly independent

Proof checking : if $A$ and $B$ are finite sets then so $A \cap B$ finite

Can you solve any induction problem with base case 0

Can this inductive proof that $\sum_{i=0}^n2^{2i+1}=\frac23(4^n-1)$ be simplified?

Prove $(1 + 1/n)^n \le n+1$

If $\frac{a}{k} - \frac{a(c-1)}{kb} > 1$, is $\frac{a}{k+1} - \frac{a(c-1)}{(k+1)b} > 1$?

Sum of all subsets of the set of even coprime integers relative to a power of a prime

Proving binomial sum using mathematical induction

Prove by mathematical induction, that $81\times 3^{2n} - 2^{2n}$ is divisible by $5$ where $n \in \mathbb{Z}^+$

Proof with binomial coefficients and induction

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