Previous problems

This page gives a list of previous biweekly problems and their respective solutions.

Previous Problem (No. 49)

Consider an ellipse ax²+by²=1 with rational a,b. Show that if there is a point on this ellipse with both coordinates rational, then there are infinitely many such points.

Solution (pdf)

PROBLEMS SINCE September 2021

All documents state the problem on the first page, with a sketch of the solution being presented on the second page.

Problem 49 (May 29-June 10, 2022): Rational points on an ellipse (pdf)
Problem 48 (May 10-24,2022): Erdős-Szekeres-theorem (pdf)
Problem 47 (Apr 19-30, 2022): Zeta(2) and Zeta(4) (pdf)
Problem 46 (Apr 01-14, 2022): Average height and average weight (pdf)
Problem 45 (Mar 19-31, 2022): A matrix equation in SL_2(Z) (pdf)
Problem 44 (Mar 01-18, 2022): Reconstruction of regular graphs (pdf)
Problem 43 (Feb 17-28, 2022): Cohn's criterion (pdf)
Problem 42 (Feb 01-16, 2022): Stamp foldings (pdf)
Problem 41 (Jan 18-31, 2022): Bounding triangle areas (pdf)
Problem 40 (Dec 17-31, 2021): Location of critical points (pdf)
Problem 39 (Nov 16-30, 2021): A convergent series (pdf)
Problem 38 (Nov 01-15, 2021): Odd-dimensional division algebras (pdf)
Problem 37 (Oct 18-31, 2021): K_10 and 3 Petersen graphs (pdf)
Problem 36 (Oct 01-15, 2021): Partitions with equal power sums (pdf)
Problem 35 (Sep 15-30, 2021): A problem by Arnold (pdf)

Problems before September 2021

Older biweekly problems have been moved to box