Question

Find all $n\in\mathbb N$ such that $10^n-6^n$ is a perfect square

score 269 · Answer 1 · 2026-03-25 00:26:49

269

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Find all $n\in\mathbb N$ such that $10^n-6^n$ is a perfect square

Published on 25 Mar 2026 - 0:26

score 558 · Answer 2 · 2026-03-27 09:48:08

558

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Sum of two perfect squares is also a perfect square. Proof that one of these numbers is divisible by 3

Published on 27 Mar 2026 - 9:48

score 52 · Answer 3 · 2020-02-02 10:11:19

$x_{n + 3} = \frac{(n + 1)(n^2 + n + 1)}{n}x_{n + 2} + (n^2 + n + 1)x_{n + 1} - \frac{n + 1}{n}x_n, n \ge 1$, $\sqrt{x_n} \in \mathbb N, n \ge 0$.

score 456 · Answer 4 · 2026-03-25 23:42:30

456

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Conjecture : an odd perfect square $n>1$ raised to the $m$-th power is never divisible by the sum of $n$'s divisors

Published on 25 Mar 2026 - 23:42

score 53 · Answer 5 · 2020-02-09 16:17:24

53

Views

Find the 5 digits number that arrange from x,x+1,x+2,3x,x+3 so that the number is a perfect square

Published on 09 Feb 2020 - 16:17

score 225 · Answer 6 · 2020-02-10 14:27:43

225

Views

Solving the sequence $a_{n+1}=a_{n}a_{n-1}+\sqrt{(a_n^2-1)(a_{n-1}^2-1)}$: proving that $2+2a_n$ is a perfect square

Published on 10 Feb 2020 - 14:27

score 1.3k · Answer 7 · 2026-03-27 09:48:08

1.3k

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Sum of squares compared to square of sum, divided by number of elements being summed

Published on 27 Mar 2026 - 9:48

score 107 · Answer 8 · 2020-02-15 17:22:42

107

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At least one perfect square in $[S_n,S_{n+1}]$

Published on 15 Feb 2020 - 17:22

score 221 · Answer 9 · 2020-02-16 10:54:03

221

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Without a calculator, prove: $7^{1/2} + 7^{1/3} + 7^{1/4} < 7$ [solved]

Published on 16 Feb 2020 - 10:54

score 586 · Answer 10 · 2026-03-26 23:10:00

586

Views

What is the term for a shape that has uniform dimensions?

Published on 26 Mar 2026 - 23:10

score 54 · Answer 11 · 2026-03-28 20:56:46

54

Views

Tribonacci Numbers Satisfying Certain Conditions

Published on 28 Mar 2026 - 20:56

score 114 · Answer 12 · 2020-02-26 17:05:01

114

Views

Prove that there are no integer solutions to $ c^2 = 2018^a + 2018^b $

Published on 26 Feb 2020 - 17:05

score 88 · Answer 13 · 2026-03-25 17:40:21

88

Views

Find all positive integers x such that $x^4-8x+16$ is a full square

Published on 25 Mar 2026 - 17:40

score 61 · Answer 14 · 2020-02-29 14:53:35

61

Views

Infinitely many squares of form 50^m - 50^n?

Published on 29 Feb 2020 - 14:53

score 137 · Answer 15 · 2026-03-29 09:57:27

137

Views

What is $\sqrt{x^2}$?

Published on 29 Mar 2026 - 9:57

List Question

Find all $n\in\mathbb N$ such that $10^n-6^n$ is a perfect square

Sum of two perfect squares is also a perfect square. Proof that one of these numbers is divisible by 3

$x_{n + 3} = \frac{(n + 1)(n^2 + n + 1)}{n}x_{n + 2} + (n^2 + n + 1)x_{n + 1} - \frac{n + 1}{n}x_n, n \ge 1$, $\sqrt{x_n} \in \mathbb N, n \ge 0$.

Conjecture : an odd perfect square $n>1$ raised to the $m$-th power is never divisible by the sum of $n$'s divisors

Find the 5 digits number that arrange from x,x+1,x+2,3x,x+3 so that the number is a perfect square

Solving the sequence $a_{n+1}=a_{n}a_{n-1}+\sqrt{(a_n^2-1)(a_{n-1}^2-1)}$: proving that $2+2a_n$ is a perfect square

Sum of squares compared to square of sum, divided by number of elements being summed

At least one perfect square in $[S_n,S_{n+1}]$

Without a calculator, prove: $7^{1/2} + 7^{1/3} + 7^{1/4} < 7$ [solved]

What is the term for a shape that has uniform dimensions?

Tribonacci Numbers Satisfying Certain Conditions

Prove that there are no integer solutions to $ c^2 = 2018^a + 2018^b $

Find all positive integers x such that $x^4-8x+16$ is a full square

Infinitely many squares of form 50^m - 50^n?

What is $\sqrt{x^2}$?

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