Solve y^2-=10(mod13)

Answer 1

Since y²≡ 10 (mod 13), we can rewrite that as:

y² = 13k + 10 by definition of mod.

Then we can manipulate it algebraically:

y = ± √(13k + 10)

Plugging in values to get a perfect square:

When k = 2, 13k + 10 = 26 + 10 = 36 = 6². Bingo.

Now we know that y = ± 6.

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