MathDB

5

Part of 2019 BMT Spring

Problems(5)

To Be-eta's or Not to Be-eta's (BMT 2019 Algebra #5)

Source:

5/5/2019
Find the sum of all real solutions to (x2−10x−12)x2+5x+2=1 (x^2 - 10x - 12)^{x^2+5x+2} = 1
Vieta
| z - 3i t| + | z - 4 | <= 5\sqrt{2}

Source: BMT 2019 Geo #5 https://artofproblemsolving.com/community/c2503497_2019_bmt_spring

12/30/2021
Find the area of the set of all points z z in the complex plane that satisfy ∣z−3i∣+∣z−4∣≤52 \left| z - 3i \right| + \left| z - 4 \right| \leq 5\sqrt{2} .
inequalitiesalgebracomplex numbersgeometry
Not Wiles' Theorem, the other one (BMT 2019 Discrete #5)

Source:

5/24/2019
Let 21110≡n mod 1111 2^{1110} \equiv n \bmod{1111} with 0≤n<1111 0 \leq n < 1111 . Compute n n .
2019 BMT Team 5

Source:

1/7/2022
What is the minimum distance between (2019,470)(2019, 470) and (21a−19b,19b+21a)(21a - 19b, 19b + 21a) for a,b∈Za, b \in Z?
algebranumber theory
max area of Q, angle between 30^o and 60^o 2019 BMT Individual 5

Source:

1/5/2022
Point PP is 3\sqrt3 units away from plane AA. Let QQ be a region of AA such that every line through PP that intersects AA in QQ intersects AA at an angle between 30o30^o and 60o60^o . What is the largest possible area of QQ?
geometryareasangles