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Number theory, biggest odd divisor, additional TST,Serbia

Source: Serbia additional TST 2016

April 5, 2016

number theory

Problem Statement

Let

w(x)

be largest odd divisor of

x

. Let

a,b

be natural numbers such that

(a,b)=1

and \\

a+w(b+1)

and

b+w(a+1)

are powers of two. Prove that

a+1

and

b+1

are powers of two.