MathDB

6. For a prime factorisation of a positive integer

N

let us call the exponent of a prime

p

the integer

k

for which

p^{k} \mid N

but

p^{k+1} \nmid N

; let, further, the power

p^{k}

be called the "contribution" of

p

N

. Show that for any positive integer

n

and for any primes

p

and

q

the contibution of

p

n!

is greater than the contribution of

q

if and only if the exponent of

p

is greater than that of

q

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