MathDB

1

Part of 2021 MMATHS

Problems(2)

MMATHS 2021, Problem 1: 20^21

Source:

10/31/2021
Suppose that 2021=2a5b=4c5d=8e5f20^{21} = 2^a5^b = 4^c5^d = 8^e5^f for positive integers a,b,c,d,e,a,b,c,d,e, and ff. Find 100bdface\frac{100bdf}{ace}.
Proposed by Andrew Wu
YaleMMATHS
MMATHS 2021, TB Problem 1: Weird Roots Sum

Source:

10/31/2021
Let a,b,ca,b,c be the roots of the polynomial x3−20x2+22.x^3 - 20x^2 + 22. Find bca2+acb2+abc2.\frac{bc}{a^2}+\frac{ac}{b^2}+\frac{ab}{c^2}.
Proposed by Deyuan Li and Andrew Milas
YaleMMATHS