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**+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)

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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)

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Melody
Mar 28, 2017