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Divisor of specific form

Source: 2007 Bulgarian Autumn Math Competition, Problem 9.4

March 17, 2022

number theoryDivisibility

Problem Statement

Find the smallest natural number, which divides

2^{n}+15

for some natural number

n

and can be expressed in the form

3x^2-4xy+3y^2

for some integers

x

and

y