Mathematics · A new problem every week
Weekly Putnam
One original problem a week, pitched at the hard end of the William Lowell Putnam Competition: the A5, B5, A6 and B6 slots, where a problem usually needs two ideas and a reformulation before it gives way.
Try the problem first. When you want it, the full worked solution is one click away: graded hints, the key idea, a complete proof, and a note on why the problem is hard.
![Putnam problem, 5 October 2026, in English and Japanese. Let f from [0,1] to the real numbers be a continuous function that is not constant, and suppose that the integral from 0 to 1 of f(x) to the power k dx is an integer for each k = 1, 2, ..., 2026. Prove that the maximum of f minus the minimum of f over [0,1] is greater than 3.99.](/weekly-putnam/putnam-weekly-2026-10-05-card.png)
This week · 5 October 2026
Integer moments need room
A continuous function whose first 2026 power integrals are all integers cannot live inside a short interval. How much room does it need, and why?
Read the full worked solution (PDF)Every week
Worked solutions · English, with Japanese editions from 3 October 2026
5 October 2026: Integer moments need room
Show that a nonconstant continuous function whose first 2026 power integrals are integers has a range wider than 3.99. Real analysis, level A5.
PDFSolutionEnglish / 日本語
3 October 2026: Five matrices that square to zero
Find every size n admitting five real square-zero matrices whose pairwise anticommutators all equal the identity. Linear algebra, level A5.
PDFSolutionEnglish / 日本語
30 September 2026: Polynomials that never meet their own shift
Count the monic f over the field with 2k elements for which f(x) and f(x+1) are coprime. Polynomials over finite fields, level B5.
PDFSolution