Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How can I calculate the fractional part $$\displaystyle \left\{\frac{22^{56}}{17}\right\}$$

Here $\displaystyle \{x\} = \text{ fractional part of $x$}$

share|cite|improve this question
up vote 5 down vote accepted

Hint: Take $22^{56}$ modulo $17$ by using Fermat's Little Theorem.

share|cite|improve this answer
Thanks Joe Zeng Got it. Fermat's Little Theorem.$a^{p-1}=a mod(p)$ where $a\;,p\in \mathbb{Z^{+}}$ and $a,p$ are relatively prime $(22)^{16} = 1mod(p)\Leftrightarrow (22)^{48}=1mod(p)$ and $(22)=5mod(17)\Leftrightarrow (22)^8 =(5)^8mod(17)=(8)^4mod(17)=(13)^2mod(17)=16mod(17)$ so $(22)^{56}=16mod(17)$ – juantheron Feb 17 '13 at 15:34
That is correct. – Joe Z. Feb 17 '13 at 21:00

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.