List questions from arithmetic

Published on 10 Apr 2026 - 12:24

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If $\frac{(b−c)}{a} + \frac{(a+c)}{b} + \frac{(a−b)}{c}=1$ and $a-b+c \neq 0 $, then prove that $\frac 1a = \frac 1b + \frac 1c$

Published on 11 Apr 2026 - 16:20

260

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How do I find two integers - $x$ and $y$ - whose values satisfy the expression $x^2 + y^2 = z$, where $z$ is a perfect square?

Published on 11 Apr 2026 - 19:48

272

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If $a+b+c+d=1$ then why is the maximum value of $(a+1)(b+1)(c+1)(d+1)$ is ${\left(\frac{5}{4}\right)}^4$?

Published on 06 Apr 2026 - 16:19

581

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How to show this fraction is not an integer

Published on 08 Apr 2026 - 22:20

7.2k

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$(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3=24xyz$?

Published on 06 Apr 2026 - 16:20

474

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Unusual result to the addition

Published on 01 Jul 2015 - 13:36

271

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Mathematical induction problem. Let $S_{n}=\left (3+\sqrt{5}\right)^{n}+\left(3-\sqrt{5}\right)^{n}$

Published on 02 Jul 2015 - 6:56

62

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Confused about proof of division

Published on 10 Apr 2026 - 15:32

891

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How to prove that $7^{31} > 8^{29}$

Published on 25 Mar 2026 - 10:53

1.7k

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Finding remainder of negative number

Published on 12 Apr 2026 - 2:00

3.3k

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Last 10 digits of the billionth fibonacci number?

Published on 07 Jul 2015 - 21:26

97

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Does $k\cdot x < y$ imply that $x \ne y$?

Published on 11 Apr 2026 - 7:12

44

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How many grams of coating is being yield per volume width?

Published on 10 Jul 2015 - 17:40

3.3k

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Negative roots of a cubic equation

Published on 07 Apr 2026 - 3:16

List Question

(Visual) Intuition: Division and complex fractions

If $\frac{(b−c)}{a} + \frac{(a+c)}{b} + \frac{(a−b)}{c}=1$ and $a-b+c \neq 0 $, then prove that $\frac 1a = \frac 1b + \frac 1c$

How do I find two integers - $x$ and $y$ - whose values satisfy the expression $x^2 + y^2 = z$, where $z$ is a perfect square?

If $a+b+c+d=1$ then why is the maximum value of $(a+1)(b+1)(c+1)(d+1)$ is ${\left(\frac{5}{4}\right)}^4$?

How to show this fraction is not an integer

$(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3=24xyz$?

Unusual result to the addition

Mathematical induction problem. Let $S_{n}=\left (3+\sqrt{5}\right)^{n}+\left(3-\sqrt{5}\right)^{n}$

Confused about proof of division

How to prove that $7^{31} > 8^{29}$

Finding remainder of negative number

Last 10 digits of the billionth fibonacci number?

Does $k\cdot x < y$ imply that $x \ne y$?

How many grams of coating is being yield per volume width?

Negative roots of a cubic equation

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