verify that both (2,6) and (0,7) satisfy y^2≡ x^3 + 4x + 20 (mod 29). we need to find whether these points satisfy the given curve .i am not sure exactly as how to proceed with the given problem. any help would be appreciated. Thank-You.
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The definition is that $y^2-x^3-4x-20$ is divisible by $29$. So, just put $x=2$ and $y=6$, compute and try to divide by $29$. Do the same with $x=0$ and $y=7$. – Apr 04 '18 at 04:23
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$(2,6)$ means $x = 2, y = 6$. Similarly, $(0, 7)$ means $x = 0$ and $y = 7$.
Therefore, you can just check if $$6^2 \equiv 2^3 + 4 \cdot 2 + 20 \pmod {29}$$ and $$7^2 \equiv 0^3 + 4 \cdot 0 + 20 \pmod {29}$$
are true.
Toby Mak
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