Difference between revisions of "2005 Alabama ARML TST Problems/Problem 6"

Revision as of 18:15, 17 November 2006

Problem

How many of the positive divisors of 3,240,000 are perfect cubes?

Solution

$3240000=2^63^45^4$ . We want to know how many numbers are in the form $2^{3a}3^{3b}5^{3c}$ , $a\leq 2$ , $b\leq 1$ , $c\leq 1$ ; there are 12 such numbers, if we count 1 as a perfect cube.

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Difference between revisions of "2005 Alabama ARML TST Problems/Problem 6"

Revision as of 18:15, 17 November 2006

Problem

Solution

Revision as of 14:50, 17 November 2006 (view source) Solafidefarms (talk \| contribs) m (typofix) ← Older edit	Revision as of 18:15, 17 November 2006 (view source) JBL (talk \| contribs) m (2005 Alabama ARML TST/Problem 6 moved to 2005 Alabama ARML TST Problems/Problem 6) Newer edit →
(No difference)