Question

How many perfect squares can be written in the form $2{a^{2}}+3{b^{2}}$ with $a, b \in \mathbb{N}$?

score 94 · Answer 1 · 2024-01-06 17:13:09

94

Views

How many perfect squares can be written in the form $2{a^{2}}+3{b^{2}}$ with $a, b \in \mathbb{N}$?

Published on 06 Jan 2024 - 17:13

score 60 · Answer 2 · 2024-01-08 18:44:19

60

Views

solution verification - determine $a, b, x$ so that $\overline{ab}^2 = \overline{xxb} $ and $\overline {ba} ^ 2 = \overline {bxx}$

Published on 08 Jan 2024 - 18:44

score 135 · Answer 3 · 2024-01-09 12:43:29

135

Views

Determine the nonzero natural numbers $a$ and $b$ for which the number $n=\sqrt{a^{2}+6b}+\sqrt{b^{2} +6a}$ is rational.

Published on 09 Jan 2024 - 12:43

score 324 · Answer 4 · 2026-03-26 06:16:36

324

Views

Except for $1$, are there any perfect powers in the sequence $1,21,321,4321,\cdots$?

Published on 26 Mar 2026 - 6:16

score 96 · Answer 5 · 2026-03-27 06:17:06

96

Views

Show that the number $2^{2^{2n+1}}+2^{2^{2n}}+1$ is not prime.

Published on 27 Mar 2026 - 6:17

score 176 · Answer 6 · 2024-01-12 13:40:32

176

Views

Find integers solutions for which bivariate polynomial with bi-quadratic form: $4x^2y^2-4xy^2+1$, becomes a square number

Published on 12 Jan 2024 - 13:40

score 87 · Answer 7 · 2024-01-18 11:38:06

Show that $\frac{2}{(x + y + z)} \left(\frac{x ^ 3}{x ^ 2 + y ^ 2} + \frac{y ^ 3}{y ^ 2 + z ^ 2} + \frac{z ^ 3}{z ^ 2 + x ^ 2}\right) \geq 1$

score 37 · Answer 8 · 2024-01-19 06:45:07

37

Views

How to proof $(x^n)' = nx^{n-1} (with \enspace n \in \mathbb{R})$?

Published on 19 Jan 2024 - 6:45

score 104 · Answer 9 · 2026-03-27 10:46:08

104

Views

Why does the term being squared in the Pythagorean triplet make no difference to the whole triplet?

Published on 27 Mar 2026 - 10:46

score 198 · Answer 10 · 2024-01-28 17:26:32

198

Views

$N$ is not a perfect square

Published on 28 Jan 2024 - 17:26

score 73 · Answer 11 · 2024-01-29 04:26:32

73

Views

Why can't I graph my summation equation for calculating perfect squares (The equation is correct, I tested it)

Published on 29 Jan 2024 - 4:26

score 83 · Answer 12 · 2024-02-03 14:44:58

83

Views

Find all non-negative integers (a,b) such that $k^{2}$a+b is perfect square for all integers k

Published on 03 Feb 2024 - 14:44

score 90 · Answer 13 · 2026-03-29 05:44:17

90

Views

Show that the number $\frac{\sqrt{2021^4+2 \cdot 2020^2-4041^2}}{505 \cdot 1011}$ is natural and a perfect cube.

Published on 29 Mar 2026 - 5:44

score 45 · Answer 14 · 2024-02-07 10:17:53

45

Views

solution verification || Show that there are at least 946 subsets of M for which the sum of their elements is a natural number.

Published on 07 Feb 2024 - 10:17

score 83 · Answer 15 · 2024-02-07 13:40:31

Determine numbers for which $\sqrt{ \frac{\overline{ab}^2 + \overline{cd}^2}{2}} = \frac{ \overline{ab} + \overline{cd}}{ 2} +1$.

List Question

How many perfect squares can be written in the form $2{a^{2}}+3{b^{2}}$ with $a, b \in \mathbb{N}$?

solution verification - determine $a, b, x$ so that $\overline{ab}^2 = \overline{xxb} $ and $\overline {ba} ^ 2 = \overline {bxx}$

Determine the nonzero natural numbers $a$ and $b$ for which the number $n=\sqrt{a^{2}+6b}+\sqrt{b^{2} +6a}$ is rational.

Except for $1$, are there any perfect powers in the sequence $1,21,321,4321,\cdots$?

Show that the number $2^{2^{2n+1}}+2^{2^{2n}}+1$ is not prime.

Find integers solutions for which bivariate polynomial with bi-quadratic form: $4x^2y^2-4xy^2+1$, becomes a square number

Show that $\frac{2}{(x + y + z)} \left(\frac{x ^ 3}{x ^ 2 + y ^ 2} + \frac{y ^ 3}{y ^ 2 + z ^ 2} + \frac{z ^ 3}{z ^ 2 + x ^ 2}\right) \geq 1$

How to proof $(x^n)' = nx^{n-1} (with \enspace n \in \mathbb{R})$?

Why does the term being squared in the Pythagorean triplet make no difference to the whole triplet?

$N$ is not a perfect square

Why can't I graph my summation equation for calculating perfect squares (The equation is correct, I tested it)

Find all non-negative integers (a,b) such that $k^{2}$a+b is perfect square for all integers k

Show that the number $\frac{\sqrt{2021^4+2 \cdot 2020^2-4041^2}}{505 \cdot 1011}$ is natural and a perfect cube.

solution verification || Show that there are at least 946 subsets of M for which the sum of their elements is a natural number.

Determine numbers for which $\sqrt{ \frac{\overline{ab}^2 + \overline{cd}^2}{2}} = \frac{ \overline{ab} + \overline{cd}}{ 2} +1$.

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