[Question]
  [
A cyclic number is a number of "n" digits that when multiplied by 1, 2, 3,...n, results in the same digits but in a different order.
For example, the number 142,857 is a cyclic number since 142,857 x 2 = 285,714, 142,857 x 3 = 428,571, 142,857 x 4 = 571,428, and so on. Given an integer input, determine if it is a cyclic number by outputting a truthy value if it is, and a falsy value if not.
Also, to be clear, the input can contain leading 0's: e.g. 0344827586206896551724137931
This is due to the fact that if leading zeros are not permitted on numerals, then 142857 is the only cyclic number in decimal.
Since it is code-golf, shortest answer in bytes wins!
  
[Answer]
# [Actually](https://github.com/Mego/Seriously), 18 bytes
```
;;ru@≈*♂$♂S♂≈╔@S≈=
```
[Try it online!](https://tio.run/##S0wuKU3Myan8/9/auqjU4VFnh9ajmU0qQBwMxEDuo6lTHIKBtO3//0oGphYWRsamRpYmhobmZibmSgA "Actually – Try It Online") (expects quoted input)
Explanation:
```
;;ru@≈*♂$♂S♂≈╔@S≈=
;;                  duplicate input twice
  ru                range(1, len(input)+1)
    @≈              convert input to an integer
      *             multiply input by each element in range
       ♂$♂S♂≈       convert each product to a string, sort the digits, and convert back to int
             ╔      uniquify: remove duplicate elements
              @S≈   sort input and convert to int
                 =  compare equality
```
[Answer]
# [05AB1E](https://github.com/Adriandmen/05AB1E), ~~9~~ 6 bytes
Thanks to *Emigna* for saving 3 bytes!
```
ā*€{ïË
```
Explanation:
```
ā        # Push range(1, len(input) + 1)
 *       # Multiply by the input
  €{     # Sort each element
    ï    # Convert to int to remove leading zeros
     Ë   # Check if all elements are equal
```
Uses the **05AB1E** encoding. [Try it online!](https://tio.run/nexus/05ab1e#BcE7EYBQDARAP1T5XC6JNiposcIMIh5KMBJ25z2277z39axrRpSN1rCAeVqVekS7mbhXl0tIIRFJS9UiIMxsUn8 "05AB1E – TIO Nexus")
[Answer]
# Python, 86 bytes
```
lambda n:all(sorted(n)==sorted(str(int(n)*i).zfill(len(n)))for i in range(2,len(n)+1))
```
[Try it online!](https://repl.it/IV8r/2)
Input numbers as strings.
[Answer]
# PHP, 64 Bytes
```
for(;$i++<9;)$r+=($c=count_chars)($argn)==$c($argn*$i);echo$r>1;
```
[Online Version](http://sandbox.onlinephpfunctions.com/code/f7a770a17415bbc9b9b3a5d484afac92e49d30a5)
[Answer]
# Haskell, 36 33 32 45 bytes
```
c n=let l=length n in(10^l-1)`div`read n==l+1
```
Example usage:
```
*Main> c "142857"
True
```
I don't think this algorithm needs any explanation.
[TOL](https://tio.run/##y0gszk7Nyfn/P1khzzYntUQhB0jmpZdkKOQpZOZpGBrE5egaaiakZJYlaORoG2ra2halJqYo5P3/DwA)
Thanks for suggestions: Generic Display Name, Laikoni.
Thanks for correction: Antony Hatchkins.
**EDIT** Nope, fails on "33".
[Answer]
# dc, 24 25 bytes
```
[1]sa0?dZd10r^1-r1+/rx=ap
```
Prints "0" if the number is not cyclic, otherwise "1". Requires the number to be entered as a string.
Example usage:
```
$ echo "[052631578947368421]" | dc -e '[1]sa0?dZd10r^1-r1+/rx=ap'
1
$ echo "[052631578947368422]" | dc -e '[1]sa0?dZd10r^1-r1+/rx=ap'
0
```
[TOL](https://tio.run/nexus/dc#@x9tGFucaGCfEpViaFAUZ6hbZKitX1Rhm1jw/z8A)
Explanation: Same algorithm as my Haskell submission.
EDIT Nope, fails on "33".
[Answer]
## Mathematica, 81 bytes
```
Length@Union@PadLeft[Sort/@IntegerDigits[ToExpression@#*Range@StringLength@#]]<2&
```
[Try it online!](https://tio.run/##y00sychMLv6fZvvfJzUvvSTDITQvMz/PISAxxSc1rSQ6OL@oRN/BM68kNT21yCUzPbOkODok37WioCi1uBikUFkrKDEvPdUhuKQoMy8daoZybKyNkdr/AKBQiYJDmoOSgYmxibmFkZmBhZmlqZmpkaG5saWhsdJ/AA "Mathics – Try It Online")
input string
**Input**
> 
> "010309278350515463917525773195876288659793814432989690721649484536082474226804123711340206185567"
> 
> 
> 
**Output**
> 
> True
> 
> 
> 
[Answer]
# [Scala 3](https://www.scala-lang.org/), 85 bytes
```
n=>(2 to n.size).forall(i=>n.sorted==(BigInt(n)*i).toString.padTo(n.size,'0').sorted)
```
[Attempt This Online!](https://ato.pxeger.com/run?1=bY-9TsMwFIXF2pEnuMpSG9Eo_ncqORLdGJigU9XBtEllFOzKMSBAfRKWMsDCE8HTEJFOqMs9uud-50j37bNb2dayr0U28eHJRp8tf05Ow-1dvUpwZZ2H1xHAum7gvl-QjZtuChcx2ufFdYrOb5Z4CnPvEpg_EmDbu6n1qEEZ4VQLlWH8_1AIrSkTtOSEKMmPI1QyIpQuuWJSc0qOQZxxpakstCyFFJQoVhJ2DGSca6qElrSQupRCEEU5Yapkh97dqB-PtoVmCmh4zVSzENraegzm4yE1E_0996ZCFFIAn3fupcZ5E6JtW-RM1TshpnptDJq5zaVPyOMzh_MUhrp8a9c3AQ3B83ExxocAHsrfd4Pu94P-Ag)
]