Number theory · Integer factorisation · Divisors · Ordering constraints · Casework
The integers \(a\), \(b\), \(c\), \(d\) satisfy \(a > b > c > d\) and
\[ (1 - a)(1 - b)(1 - c)(1 - d) = 10 . \]
Which values can the expression \(a + b - c - d\) take?
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2010, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source