+0  
 
0
98
5
avatar

Given that $13^{-1} \equiv 29 \pmod{47}$, find $34^{-1} \pmod{47}$, as a residue modulo 47. (Give a number between 0 and 46, inclusive.)

 Jun 4, 2021
 #1
avatar+2205 
+1

Looking at this problem, the first thing that I notice is that 13 + 37 = 47. 

34 = -13 (mod 47)

13^(-1) = 29 (mod 47)

-13^(-1) = -29 (mod 47)

-29 = 18 (mod 47)

 

=^._.^=

 Jun 4, 2021
 #2
avatar+114485 
+1

13 + 37 = 47  ???

 Jun 4, 2021
 #3
avatar+2205 
+1

Oops, I meant 34 not 37. 

13+34 = 47. 

Thank you for noticing. 

 

=^._.^=

catmg  Jun 4, 2021
 #4
avatar+114485 
+1

I figured that is what you meant.   wink

Melody  Jun 4, 2021
 #5
avatar
+1

Thx Guys!

 Jun 4, 2021

38 Online Users