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how to calculate 14^15 mod 15

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14^15 mod 15

Guest Jun 23, 2017
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#1
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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
+89633
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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
#6
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You calculated 14^15 twice and concatenated them together!! On the 2.0Webcalc: 14^15 =

155,568,095,557,812,224 mod 15 = 14.

Guest Jun 24, 2017
#7
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How do you know she calculated it twice?

It’s obviously pasted it twice, but calculated twice, you can’t know that.

You know, it would be great if you jumped into a crocodile pit. Really great!

Guest Jun 24, 2017
#2
+1

1415+1=(14+1)(1414-1413+1412-......-14+1)=15*(1414-1413+1412-......-14+1)= 1415+1 is divisible by 15

therefore, 1415 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
#3
+89633
+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
+18281
0

how to calculate 14^15 mod 15

heureka  Jun 26, 2017

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