Mastodawn

Problem for June 7th from the 2026 AMS Daily Epsilon of Math Calendar

Problem for June 6th from the 2026 AMS Daily Epsilon of Math Calendar

Working in N^p, I have two sets of vectors, u_1,...,u_n and v_1,...,v_m. I'm looking for linear sets of scalars, x_1,....x_n and y_1,...,y_n where

\sum x_i u_i = \sum y_j v_j.

i.e., Ux = Vy (collapsing to a matrix/vector representation).

There's a trivial solution (x_i=y_j=0), but I'm not entirely sure how to find the non-trivial solutions, given that it's all natural numbers.

Any pointers to keywords I can follow up on? A name for the problem?

Problem for June 5th from the 2026 AMS Daily Epsilon of Math Calendar

"real estate" implies the existence of imaginary estate and complex estate.

Problem for June 4th from the 2026 AMS Daily Epsilon of Math Calendar

Problem for June 3rd from the 2026 AMS Daily Epsilon of Math Calendar

Problem for June 2nd from the 2026 AMS Daily Epsilon of Math Calendar

Problem for June 1st from the 2026 AMS Daily Epsilon of Math Calendar

Problem for May 31st from the 2026 AMS Daily Epsilon of Math Calendar