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find real a such that 3 < a < 4 and a(a-3{a}) is an integer.

Source: CRMO 2015 region 1 p6

September 30, 2018
number theoryfractional partInteger

Problem Statement

Find all real numbers aa such that 3<a<43 < a < 4 and a(aāˆ’3{a})a(a-3\{a\}) is an integer.
(Here {a}\{a\} denotes the fractional part of aa.)
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