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.
+118608 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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