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n = 3t(n) + 5r(n), greatest odd divisor, smallest pos. divisor unequal to 1

Source: Dutch BxMO TST 2016 p1

August 24, 2019

number theorydivisoroddequation

Problem Statement

For a positive integer

n

that is not a power of two, we define

t(n)

as the greatest odd divisor of

n

and

r(n)

as the smallest positive odd divisor of

n

unequal to

1

. Determine all positive integers

n

that are not a power of two and for which we have

n = 3t(n) + 5r(n)