Solve x^2+3x+17\equiv 0\pmod{315}

p3sa1bynn

p3sa1bynn

Answered question

2022-04-27

Solve x2+3x+170±mod315

Answer & Explanation

otposlati9u8

otposlati9u8

Beginner2022-04-28Added 19 answers

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

 x2+3x+170 (mod 315)

4x2+12x+680 (mod 315)

(2x+3)2256=162 (mod 315)
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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