MathDB

11

Part of 2019 Durer Math Competition Finals

Problems(2)

min LCM of distinct a, b, c, d if a + b + c + d = 1000

Source: 2019 Dürer Math Competition Finals Day2 E11 E+10 https://artofproblemsolving.com/community/c1621835_2019_

1/5/2022
What is the smallest possible value of the least common multiple of a,b,c,da, b, c, d if we know that these four numbers are distinct and a+b+c+d=1000a + b + c + d = 1000?
least common multipleLCMnumber theory
\sum_{k=1}^{N} k^{2018} is divisible by 2018?

Source: 2019 Dürer Math Competition Finals Day2 E+11 https://artofproblemsolving.com/community/c1621835_2019_

1/5/2022
What is the smallest NN for which ∑k=1Nk2018\sum_{k=1}^{N} k^{2018} is divisible by 20182018?
Sumdividesdivisiblenumber theory