Asked by sdvds
Find the smallest positive integer N that satisfies all of the following conditions:
• N is a square.
• N is a cube.
• N is an odd number.
• N is divisible by twelve prime numbers.
How many digits does this number N have?
• N is a square.
• N is a cube.
• N is an odd number.
• N is divisible by twelve prime numbers.
How many digits does this number N have?
Answers
Answered by
mathhelper
The trouble is the divisibility by the first 12 prime numbers,
so it must be a multiple of 2*3*5*7*11*13*17*19*23*29*31*37
To be odd it must look like 2K+1
to be a square it must look like (2K+1)^2, and it must also be a cube
it must contain (2K+1)^6
so, it must have the form:
2*3*5*7*11*13*17*19*23*29*31*37(2K+1)^6
when K = 0, we get
2*3*5*7*11*13*17*19*23*29*31*37(1)^6
= 7.420738135... x 10^12
which would be 13 digits long
so it must be a multiple of 2*3*5*7*11*13*17*19*23*29*31*37
To be odd it must look like 2K+1
to be a square it must look like (2K+1)^2, and it must also be a cube
it must contain (2K+1)^6
so, it must have the form:
2*3*5*7*11*13*17*19*23*29*31*37(2K+1)^6
when K = 0, we get
2*3*5*7*11*13*17*19*23*29*31*37(1)^6
= 7.420738135... x 10^12
which would be 13 digits long
Answered by
oobleck
to be odd, it cannot have 2 as a factor.
Answered by
mathhelper
Of course, good checkup oobleck.
Answered by
sdvds
are you sure, you answerd all the points of it.
Answered by
sdvds
Please anser my question. Urgent!
If any one can solve; please do and share the answer in step by step.
If any one can solve; please do and share the answer in step by step.
Answered by
mathhelper
obviously we have to take out the factor of 2 since multiplying anything
by 2 would make it even, so
3*5*7*11*13*17*19*23*29*31*37
by 2 would make it even, so
3*5*7*11*13*17*19*23*29*31*37
Answered by
It Girl
Hey 👋
Answered by
sdvds
Please answer the question in detail.
In step by step.
Answer full, not hints.
Please Answer ASAP.
In step by step.
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Answered by
tony
I understand your approach; thanks
Answered by
sdvds
Please answer the question in detail.
In step by step.
Answer full, not hints.
Please Answer ASAP
In step by step.
Answer full, not hints.
Please Answer ASAP
Answered by
Komal battu
12/3/2008
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