Number theory · Integer factorisation · Divisors · Ordering constraints · Casework
Problem 1, 2010
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?
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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