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At most one factorization of m into the integers ab

Source: Baltic Way 1999

December 23, 2010
modular arithmeticnumber theory proposednumber theory

Problem Statement

Let mm be a positive integer such that m=2(mod4)m=2\pmod{4}. Show that there exists at most one factorization m=abm=ab where aa and bb are positive integers satisfying 0<a−b<5+44m+10<a-b<\sqrt{5+4\sqrt{4m+1}}
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