I see you like equations

The sum of three consecutive integers is equal to their product. Find all the possible set of integers with this property.

#Combinatorics

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Let them be $a-1,a,a+1$ . $(a-1)+a+(a+1)=(a-1)a(a+1)$ $\implies 3a=a(a^2-1)$ $\implies a(a^2-4)=0$ $\implies a=0,\pm 2$ Hence the set is $\{(-1,0,1),(-3,-2,-1),(1,2,3)\}$ .

Rishabh Jain - 3 years, 4 months ago

I will tell one. The smallest set would be (-1,0,1) Find the rest.

इश्वर बस्याल - 3 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$