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Source: IBEROAMERICAN 2004, Problem 3

September 22, 2004

modular arithmeticinductionquadraticsfunctionnumber theory unsolvednumber theory

Problem Statement

Let

n

and

k

be positive integers such as either

n

is odd or both

n

and

k

are even. Prove that exists integers

a

and

b

such as GCD(a,n) \equal{} GCD(b,n) \equal{} 1 and k \equal{} a \plus{} b