#1**0 **

14^15 mod 15 = 14. Use the calculator here. First calculate: 14^15 and then press "mod" key followed by 15. You should get 14 as the remainder.

Guest Jun 23, 2017

#5**+1 **

I shall try your method:)

14^15 = 155568095557812224155568095557812224mod15 = 155568095557812224*mod15

As you can see this calculator does not work that way.

I shall try putting it in properly - and yes this calculator is capable of calculating it straight up

(I had thought the number , i mean 14^15, might be too big but it is not)

mod(14^15,15) = 14

I result is directly from the web2 calc on this posting page :)

Melody
Jun 24, 2017

#2**+1 **

14^{15}+1=(14+1)(14^{14}-14^{13}+14^{12}-......-14+1)=15*(14^{14}-14^{13}+14^{12}-......-14+1)= 14^{15}+1 is divisible by 15

therefore, 14^{15} mod 15=15-1=14

Another way to solve it is this one:

\( {14}^{15}={(15-1)}^{15}={15}^{15}*\begin{pmatrix} 15\\ 0 \end{pmatrix} -{15}^{14}*\begin{pmatrix} 15\\ 1 \end{pmatrix} +.....+15*\begin{pmatrix} 15\\ 14 \end{pmatrix}- 1*\begin{pmatrix} 15\\ 15 \end{pmatrix}=15*({15}^{14}*\begin{pmatrix} 15\\ 0 \end{pmatrix}- {15}^{13}*\begin{pmatrix} 15\\ 1 \end{pmatrix}+....+1*\begin{pmatrix} 15\\ 14 \end{pmatrix})-1\)

Guest Jun 24, 2017

edited by
Guest
Jun 24, 2017

edited by Guest Jun 24, 2017

edited by Guest Jun 24, 2017

#3**+1 **

Here is another way

14^1=14= -1mod15

14^2=196= +1 mod15

14^3=2744 = mod(2744,15) = 14 = -1

114^4 = 38416 = mod(38416,15) = 1

We have a pattern

\(For\;\;n\in \text{Positive integers}\\ 14^{2n}=+1\\ 14^{2n-1}=-1 \\ so\\ 14^{15}\;\;mod\;15=-1\;\;or\;\;14\)

Melody
Jun 24, 2017

#8**0 **

**how to calculate 14^15 mod 15**

see link: https://web2.0calc.com/questions/i-have-the-same-problem-like-the-guest#r4

heureka
Jun 26, 2017