Solve \(\displaystyle{x}^{{2}}+{3}{x}+{17}\equiv{0}\pm{o}{d}{\left\lbrace{315}\right\rbrace}\)

basura8w081

basura8w081

Answered question

2022-03-20

Solve x2+3x+170(mod315)

Answer & Explanation

kanonickiuoeh

kanonickiuoeh

Beginner2022-03-21Added 8 answers

x2+3x+170(mod5,7,9)
can only have 5,7 or 9 solutions. Try all of them.
Alternately:

 x2+3x+170(mod315)

4x2+12x+680(mod315)

(2x+3)2256=162(mod315)
You can immediatelly see that 16,-16 are square roots of 256, which immediately tells you that there are at least 2 solutions. Since 3,5,7 do not divide 256 it is easy to deduce that there must be 8 solutions, you just need to find the rest.

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