Open Neighborhood Seminar: Sums of two cubes
SEMINARS, OPEN NEIGHBORHOOD
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April 5, 2023 4:30 pm - 5:30 pm
Science Center 507
Address:
1 Oxford Street, Cambridge, MA 02138 USA
Speaker:
Levent Alpöge - Harvard
I will connect the following questions and answers.
1. 42 = (12602123297335631)^3 + (80435758145817515)^3 + (-80538738812075974)^3.
2. https://people.math.harvard.
Are there positive integers x, y, z such that:
x / (y + z) + y / (x + z) + z / (x + y) = 4?
3. The Birch and Swinnerton-Dyer conjecture.
4. Hilbert's tenth problem, aka:
Is there a computer program which "solves all Diophantine equations"?
5. 0% of integers are a sum of two squares (integral or rational).
6. A positive proportion of integers are a sum of two rational cubes.
For more information, please see: https://people.math.harvard.edu/~ana/ons/