1
Part of 2020 Tuymaada Olympiad
Problems(2)
Represent as m+t_m
Source: 2020 Tuymaada Junior P1
10/6/2020
For each positive integer let be the smallest positive integer not dividing . Prove that there are infinitely many positive integers which can not be represented in the form .(A. Golovanov)
number theory
absolute greater than 2020
Source: Tuymaada 2020 Senior, Problem 1
10/6/2020
Does the system of equation
\begin{align*}
\begin{cases}
x_1 + x_2 &= y_1 + y_2 + y_3 + y_4 \\
x_1^2 + x_2^2 &= y_1^2 + y_2^2 + y_3^2 + y_4^2 \\
x_1^3 + x_2^3 &= y_1^3 + y_2^3 + y_3^3 + y_4^3
\end{cases}
\end{align*}
admit a solution in integers such that the absolute value of each of these integers is greater than ?
number theoryequationsalgebrasystem of equations