### Failure of strong approximation on an affine cone

Heilbronn Number Theory Seminar

4th October 2017, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

The equation X_0^2 + 47 X_1^2 = 103 X_2^2 + 82297 X_3^2 has

the following curious property: of its solutions modulo 17, only half

can be lifted to a solution in coprime integers. I will show how to

explain this phenomenon using the Brauer-Manin obstruction to strong

approximation on the punctured affine cone described by the equation.

This is joint work with Ivo Kok.

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