MathDB

1

Part of 2018 Stanford Mathematics Tournament

Problems(3)

7 does not divide a + b if 7 divides a^2 + b^2 + 1

Source: 2018 SMT - Stanford Math Tournament , Team Round, Proof Question 1

1/26/2022
Prove that if 77 divides a2+b2+1a^2 + b^2 + 1, then 77 does not divide a+ba + b.
number theorydividesdivisible
SMT 2018 Geometry #1 semicircle

Source:

8/8/2023
Consider a semi-circle with diameter ABAB. Let points CC and DD be on diameter ABAB such that CDCD forms the base of a square inscribed in the semicircle. Given that CD=2CD = 2, compute the length of ABAB.
geometry
SMT 2018 Geometry Tiebreaker #1

Source:

8/8/2023
Point EE is on side CDCD of rectangle ABCDABCD such that CEDE=25.\frac{CE}{DE} =\frac{2}{5}. If the area of triangle BCEBCE is 3030, what is the area of rectangle ABCDABCD?
geometry