let be positive integers with

and then

(1)

if and only if , .

(2)

if and only if , .

is it correct ?

the one way in each case is obvious. the other way...?

plz help.

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- Jan 22nd 2009, 10:52 PMthipplipowers and factorials
let be positive integers with

and then

(1)

if and only if , .

(2)

if and only if , .

is it correct ?

the one way in each case is obvious. the other way...?

plz help. - Jan 24th 2009, 03:22 AMLaurent
Note that , and is not divisible by (except if and , but remember ). As a consequence, is the largest number such divides . Can you see why this answers your question ?

Quote:

(2)

if and only if , .

- Feb 2nd 2009, 03:21 AMthippliThank you
First answer is very clear. Thank you very much !

But I think the second won't work , because

.

Here may divide . In this case how can we say is the largest integer which divides

? - Feb 3rd 2009, 03:25 AMLaurent