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Home > College Algebra calculators > Modulo example
5. Modulo example ( Enter your problem )
( Enter your problem )
  1. Example-1 : `3^302 mod 5`
  2. Example-2 : `19^24 mod 21`
  3. Example-3 : `7^106 mod 143`
  4. Example-4 : `27^400 mod 619`
 		Other related methods
  1. Chinese Remainder Theorem
  2. Extended Euclidean Algorithm
  3. Euclid's Algorithm
  4. Modular multiplicative inverse
  5. Modulo
  6. Fast modular exponentiation
1. Example-1 : `3^302 mod 5`
(Previous example)		3. Example-3 : `7^106 mod 143`
(Next example)

2. Example-2 : `19^24 mod 21`


19^24 mod 21

Solution:
`19^24" mod "21`

Here `19^24=(19^2)^12`

`=(19^2" mod "21)^12" mod "21`

`=(361" mod "21)^12" mod "21`

`=4^12" mod "21`

Here `4^12=(4^3)^4`

`=(4^3" mod "21)^4" mod "21`

`=(64" mod "21)^4" mod "21`

`=1^4" mod "21`

`=1" mod "21`

`=1`

This material is intended as a summary. Use your textbook for detail explanation.
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1. Example-1 : `3^302 mod 5`
(Previous example)		3. Example-3 : `7^106 mod 143`
(Next example)


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