+0  
 
0
522
1
avatar

A) We are given that $a^2 \equiv 4^2 \pmod{10}$ and that  $a \neq 4$ Find the value of  a. Express your answer as a residue between 0 and the modulus.

B) Let $a \neq 0$ and $a^2 \equiv 0 \pmod{12}$  What is the value of a? Express your answer as a residue between 0 and the modulus.

Guest Mar 28, 2017
 #1
avatar+92751 
+1

A) We are given that \( a^2 \equiv 4^2 \pmod{10}\)

and that  \(a \neq 4\)

Find the value of  a. Express your answer as a residue between 0 and the modulus.

 

4^2=16=6 (mod 10)

If any number ending in 4 or 6 is squared, the answer will end in a 6 and will therefor be  6 (mod10)

so a can be 6,14,16,24,26, .....

I t hink the question means that a cannot equal 4 (mod 10) so the answer must bew 6 (mod 10)

 

a = 6 (mod10)

 

----------------------------------------------------

 

B) Let    \(a \neq 0\)

and      \(a^2 \equiv 0 \pmod{12}  \)

 

What is the value of a? 

12 times table 12,24,36, 48,60,72,84,96, 108,120,132,144,

Express your answer as a residue between 0 and the modulus.

a=6,     a=12=0(mod12)

 

a=6 (mod12)

----------------------------------------------------

Melody  Mar 28, 2017

15 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.