Question

Determine all the integers $x$ that have the property that $\sqrt{x^2+7x+21}$ is a rational number.

score 195 · Answer 1 · 2024-02-20 14:12:02

195

Views

Determine all the integers $x$ that have the property that $\sqrt{x^2+7x+21}$ is a rational number.

Published on 20 Feb 2024 - 14:12

score 167 · Answer 2 · 2024-02-22 16:50:35

167

Views

Can $4\cdots41$ (with odd number of $4$s) be a Square Number?

Published on 22 Feb 2024 - 16:50

score 101 · Answer 3 · 2024-02-25 14:02:20

101

Views

Find $n\in N$ for which $2[\frac{1^2}{2}]+2^2[\frac{2^2}{3}]+...+2^n*[\frac{n^2}{ n+1}]$

Published on 25 Feb 2024 - 14:02

score 77 · Answer 4 · 2024-02-25 15:52:43

77

Views

how many natural numbers require at least 6 terms to express as the sum of distinct squares?

Published on 25 Feb 2024 - 15:52

score 85 · Answer 5 · 2024-02-26 08:19:19

85

Views

How to prove the existence of this progression? Struggling with a BDMO problem.

Published on 26 Feb 2024 - 8:19

score 69 · Answer 6 · 2024-03-04 11:25:30

Show that if $x + y + z = xy + xz + yz$ then $x ^ 2 * (1 - y ^ 2) + y ^ 2 * (1 - z ^ 2) + z ^ 2 * ( 1 - x ^ 2) = 2(x + y + z)(xyz - 1)$

score 101 · Answer 7 · 2026-03-30 11:59:26

101

Views

Find the perfect squares of four digits whose square root is the sum of the numbers obtained if we separate the first two digits from the last two

Published on 30 Mar 2026 - 11:59

score 50 · Answer 8 · 2026-02-23 10:20:48

50

Views

Is it true that for any positive integer $n$, there exists an integer $x$ where there are at least $n$ primes between $x^2$ and $(x+1)^2$

Published on 23 Feb 2026 - 10:20

score 40 · Answer 9 · 2026-03-26 04:35:01

40

Views

Is $k=11$ the largest value of $k$ such that $(\lfloor\sqrt{1!+2!+3!+\cdots+k!}\rfloor+1)^{2} - (1!+2!+3!+\cdots+k!)$ is a perfect power?

Published on 26 Mar 2026 - 4:35

score 86 · Answer 10 · 2024-03-26 13:13:15

86

Views

For which integers $n$ will $2n^2+1$ be a perfect square?

Published on 26 Mar 2024 - 13:13

score 3.3k · Answer 11 · 2026-03-30 12:00:18

3.3k

Views

Numbers $n$ such that the digit sum of $n^2$ is a square

Published on 30 Mar 2026 - 12:00

score 84 · Answer 12 · 2026-03-27 06:17:02

84

Views

General term of a series that subtracts the square root of every square.

Published on 27 Mar 2026 - 6:17

score 1.1k · Answer 13 · 2015-01-09 19:41:47

1.1k

Views

Sum of a Sequence of Prime Powers $p^{2n}+p^{2n-1}+\cdots+p+1$ is a Perfect Square

Published on 09 Jan 2015 - 19:41

score 129 · Answer 14 · 2015-01-13 17:19:35

129

Views

Find two integers $a, b$ for given integer $c$, so that $c=a^2\pm b^2$

Published on 13 Jan 2015 - 17:19

score 233 · Answer 15 · 2015-01-20 23:51:55

233

Views

Square Roots with Exponents

Published on 20 Jan 2015 - 23:51

List Question

Determine all the integers $x$ that have the property that $\sqrt{x^2+7x+21}$ is a rational number.

Can $4\cdots41$ (with odd number of $4$s) be a Square Number?

Find $n\in N$ for which $2[\frac{1^2}{2}]+2^2[\frac{2^2}{3}]+...+2^n*[\frac{n^2}{ n+1}]$

how many natural numbers require at least 6 terms to express as the sum of distinct squares?

How to prove the existence of this progression? Struggling with a BDMO problem.

Show that if $x + y + z = xy + xz + yz$ then $x ^ 2 * (1 - y ^ 2) + y ^ 2 * (1 - z ^ 2) + z ^ 2 * ( 1 - x ^ 2) = 2(x + y + z)(xyz - 1)$

Find the perfect squares of four digits whose square root is the sum of the numbers obtained if we separate the first two digits from the last two

Is it true that for any positive integer $n$, there exists an integer $x$ where there are at least $n$ primes between $x^2$ and $(x+1)^2$

Is $k=11$ the largest value of $k$ such that $(\lfloor\sqrt{1!+2!+3!+\cdots+k!}\rfloor+1)^{2} - (1!+2!+3!+\cdots+k!)$ is a perfect power?

For which integers $n$ will $2n^2+1$ be a perfect square?

Numbers $n$ such that the digit sum of $n^2$ is a square

General term of a series that subtracts the square root of every square.

Sum of a Sequence of Prime Powers $p^{2n}+p^{2n-1}+\cdots+p+1$ is a Perfect Square

Find two integers $a, b$ for given integer $c$, so that $c=a^2\pm b^2$

Square Roots with Exponents

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