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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
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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,

a=6,     a=12=0(mod12)

a=6 (mod12)

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Melody  Mar 28, 2017