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Public key 3, 4 fits the equation of y^2 = x^2 + 7

Yet this comes up as an "invalid public key". How is that invalid? Sure, it deviates extremely from other numbers, but what other equations are being applied to the public key to determine its validity?

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    The formula is y^2 = x^3 + 7. I don't think there are any small-number solutions. – Pieter Wuille Jul 13 '14 at 18:45
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    Not sure this is what you are talking about, but apparently y^2=x^3+7 has no integral solutions. – Murch Jul 14 '14 at 15:05
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    That's OK because secp256k1 doesn't just use plain integers, the equation above is evaluated with integers modulo a very large prime N. Really the equation is: y^2 = x^3 + 7 mod N. – David Grayson Feb 2 '15 at 18:46
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You got the formula wrong.

The correct formula is

y2 = x3 + 7 mod N

where N is a very large prime.

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