List questions from square-numbers

Published on 30 Mar 2026 - 3:52

86

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How do I prove that $\sqrt{9+4k^2}$ holds integer value only for $k=0$ and $k=2$?

Published on 12 Jun 2016 - 20:29

105

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Find the $m$ such $a_{n+1}=a^5_{n}+487$

Published on 15 Jun 2016 - 5:09

1.1k

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Prove that for some $x, y \in \mathbb{Z}^+$, if $(x-1)(y-1), xy, (x+1)(y+1)$ are all squares then $x = y$.

Published on 16 Jun 2016 - 10:40

216

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Find all $(x,y) \in \mathbb{N} \times \mathbb{N}$ such that $5^{x}+3^{y}$ is a perfect square

Published on 16 Jun 2016 - 14:55

177

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$n=a^2-b^2$ iff $n \not\equiv 2(\mathrm{mod\ }4)$

Published on 22 Jun 2016 - 18:29

93

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What is the first square in the sequence $4729494n+1$?

Published on 24 Jun 2016 - 12:24

127

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No square has a decimal expansion ending in 79

Published on 28 Mar 2026 - 4:34

23

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Existence of a Repeating Divisor

Published on 25 Jun 2016 - 16:17

87

Views

For which integers $q \ge p\ge 1$ with $q^2-2p^2=2$ is $2p^2+1 \pm pq$ an integer square?

Published on 27 Jun 2016 - 2:19

53

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Why are the solutions of the equation different? : $x=2 => x^2=4 => x=±2$

Published on 27 Jun 2016 - 6:42

1.3k

Views

Prove That $n(n+1)$ Can Never Be a Square Number by Showing the Atleast One of Exponents in the Prime Power Decomposition Isn't Even

Published on 27 Jun 2016 - 19:33

498

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Deciding if a number is a square in $\Bbb Z/n\Bbb Z$

Published on 26 Mar 2026 - 1:34

1.3k

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Prove that if $a, b, c$ are positive odd integers, then $b^2 - 4ac$ cannot be a perfect square.

Published on 05 May 2013 - 21:15

442

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Can both $x^2 + y+2$ and $y^2+4x$ be squares?

Published on 07 May 2013 - 4:51

List Question

Consecutive Square Numbers

How do I prove that $\sqrt{9+4k^2}$ holds integer value only for $k=0$ and $k=2$?

Find the $m$ such $a_{n+1}=a^5_{n}+487$

Prove that for some $x, y \in \mathbb{Z}^+$, if $(x-1)(y-1), xy, (x+1)(y+1)$ are all squares then $x = y$.

Find all $(x,y) \in \mathbb{N} \times \mathbb{N}$ such that $5^{x}+3^{y}$ is a perfect square

$n=a^2-b^2$ iff $n \not\equiv 2(\mathrm{mod\ }4)$

What is the first square in the sequence $4729494n+1$?

No square has a decimal expansion ending in 79

Existence of a Repeating Divisor

For which integers $q \ge p\ge 1$ with $q^2-2p^2=2$ is $2p^2+1 \pm pq$ an integer square?

Why are the solutions of the equation different? : $x=2 => x^2=4 => x=±2$

Prove That $n(n+1)$ Can Never Be a Square Number by Showing the Atleast One of Exponents in the Prime Power Decomposition Isn't Even

Deciding if a number is a square in $\Bbb Z/n\Bbb Z$

Prove that if $a, b, c$ are positive odd integers, then $b^2 - 4ac$ cannot be a perfect square.

Can both $x^2 + y+2$ and $y^2+4x$ be squares?

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