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Danube Mathematical Competition 2007 Problem 3

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

December 8, 2007
inductionnumber theory proposednumber theory

Problem Statement

For each positive integer n n, define f(n) f(n) as the exponent of the 2 2 in the decomposition in prime factors of the number n! n!. Prove that the equation n\minus{}f(n)\equal{}a has infinitely many solutions for any positive integer a a.
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