Sum-free sets of integers
Sum-free sets of integers
A set<italic>S</italic>of integers is said to be sum-free if<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a comma b element-of upper S"><mml:semantics><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo>∈<!-- ∈ --></mml:mo><mml:mi>S</mml:mi></mml:mrow><mml:annotation encoding="application/x-tex">a,b \in S</mml:annotation></mml:semantics></mml:math></inline-formula>implies<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a plus b not-an-element-of upper S"><mml:semantics><mml:mrow><mml:mi>a</mml:mi><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:mo>∉<!-- ∉ --></mml:mo><mml:mi>S</mml:mi></mml:mrow><mml:annotation encoding="application/x-tex">a + b \notin S</mml:annotation></mml:semantics></mml:math></inline-formula>. In this paper, we investigate two new problems on sum-free sets: (1) Let<inline-formula …