Show that if a and b are positive irrational numbers such that 1/a + 1/b = 1, then every positive integer can be uniquely expressed as either ?ka? or ?kb? for some positive integer k.

SolutionStep 1In this problem, we have to show that if two positive irrational number such that = 1 where a and b are irrational number.Step 2Proof by ContradictionLet us assume that A(p, n) be the set of positive integer then is less than or equal to n where x be an positive integer.It is given that have a unique value and a and b are irrational number.So, according to the property of floor function If a is...