Find the smallest positive integer N

Find the smallest positive integer N

Postby Guest » Sat Nov 20, 2021 12:25 pm

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?


Please Explain your steps in detail.
Guest
 

Re: Find the smallest positive integer N

Postby Guest » Sun Dec 05, 2021 2:28 am

The number has to be the 6th power of an integer.
It has to be the product of odd numbers.
Its prime factors are exactly 12.
The lowest integer is therefore
[tex](3\cdot 5\cdot 7\cdot 11\cdot 13\cdot 17\cdot 19\cdot 23\cdot 29\cdot 31\cdot 37\cdot 41)^{6}[/tex]
and it has 86 digits.
Guest
 


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