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Find the remainder when 15^145 is divided by 26.

 Oct 26, 2019
 #1
avatar+2417 
+2

Look at guest answer belwo

 

I attempted it, but somehow got 19. Rip.

 Oct 26, 2019
edited by CalculatorUser  Oct 26, 2019
edited by CalculatorUser  Oct 26, 2019
 #2
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+2

15^145 mod 26 = 15

 

If you do the actual division, this is what you should get:

 

15^145 / 26 =1312983338 7719885766 1024601110 7556846410 9960169490 7167019486 7931722744 5648476512 7652340511 7917837585 4355823111 0988664260 7746973976 4592875193 1985691324 0913015145 5218975360.576 923 076 923 .

 

If you multiply the fraction 0.576 923 076 923 x 26 = 15 - which is the remainder.

 Oct 26, 2019
edited by Guest  Oct 26, 2019
 #3
avatar+4325 
0

A faster way is the Euler's Theorem.

phi26=12 and 15^145phi12=15^1=15.

 Oct 27, 2019
 #4
avatar+236 
+1

I attempted it this way. We know that 15^145 = 15^5(29). I then took 15^5 mod 26, or 19. Then, I took 19^29 mod 26, which gave me 15.

 Oct 27, 2019

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