MathDB

3

Part of 1977 Bundeswettbewerb Mathematik

Problems(2)

Bundeswettbewerb Mathematik 1977 Problem 1.3

Source: Bundeswettbewerb Mathematik 1977 Round 1

10/10/2022
The number 5050 is written as a sum of several positive integers (not necessarily distinct) whose product is divisible by 100.100. What is the largest possible value of this product?
Integersalgebranumber theory
Bundeswettbewerb Mathematik 1977 Problem 2.3

Source: Bundeswettbewerb Mathematik 1977 Round 2

10/10/2022
Show that there are infinitely many positive integers aa that cannot be written as a=a16+a26+…+a76,a = a_{1}^{6}+ a_{2}^{6} + \ldots + a_{7}^{6}, where the aia_i are positive integers. State and prove a generalization.
number theoryinfinitely many solutionsIntegersGeneralization