MathDB

24

Part of 2021 BMT

Problems(2)

BMT 2021 Guts Round p24

Source:

10/7/2022
Suppose that a,b,ca, b, c, and p are positive integers such that pp is a prime number and a2+b2+c2=ab+bc+ca+2021pa^2 + b^2 + c^2 = ab + bc + ca + 2021p. Compute the least possible value of max⁡ (a,b,c)\max \,(a, b, c).
algebrainequalitiesnumber theory
BMT 2021 General p24

Source:

9/27/2023
Given that x,yx, y, and zz are a combination of positive integers such that xyz=2(x+y+z)xyz = 2(x + y + z), compute the sum of all possible values of x+y+zx + y + z.
number theory