Find a natural number n, in canonical form, such than n/2=a^2 , n/3=b^3 , n/5= c^5 for some a,b,c (natural numbers)

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- Mar 27th 2013, 02:47 AMuserit8find n such that...
Find a natural number n, in canonical form, such than n/2=a^2 , n/3=b^3 , n/5= c^5 for some a,b,c (natural numbers)

- Mar 27th 2013, 05:22 AMNehushtanRe: Find n such that …
$\displaystyle n$ is divisible by 2, 3, and 5, so try $\displaystyle n=2^r3^s5^t$. Then $\displaystyle r$ must be divisible by 3 and 5, $\displaystyle s$ must be divisible by 2 and 5, and $\displaystyle t$ must be divisible by 2 and 3. Hence one possible value for $\displaystyle n$ is $\displaystyle 2^{15}3^{10}5^{6}$.