MathDB

3

Part of 2021 MMATHS

Problems(2)

MMATHS 2021, TB Problem 3: Log Product

Source:

10/31/2021
Find the sum of all xx from 22 to 10001000 inclusive such that ∏n=2xlog⁡nn(n+1)n+2\prod_{n=2}^x \log_{n^n}(n+1)^{n+2} is an integer.
Proposed by Deyuan Li and Andrew Milas
YaleMMATHS
MMATHS 2021, Problem 3: Mislabeled Dodecagon

Source:

10/31/2021
Let ABCDEFABCDEF be a regular hexagon with sidelength 66, and construct squares ABGHABGH, BCIJBCIJ, CDKLCDKL, DEMNDEMN, EFOPEFOP, and FAQRFAQR outside the hexagon. Find the perimeter of dodecagon HGJILKNMPORQHGJILKNMPORQ.
Proposed by Andrew Wu
MMATHS