3

Part of 2007 Danube Mathematical Competition

Problems(1)

Danube Mathematical Competition 2007 Problem 3

Source: consequence of a classical result about exponent of primes in factorials

For each positive integer

n

f(n)

as the exponent of the

2

in the decomposition in prime factors of the number

n!

. Prove that the equation n\minus{}f(n)\equal{}a has infinitely many solutions for any positive integer

a

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