How about the maximum power of 2?

Number Theory Level 3

The product of any 2 consecutive positive integers must be divisible by $2^{1}$ .
The product of any 4 consecutive positive integers must be divisible by $2^{1+2}$ .
The product of any 8 consecutive positive integers must be divisible by $2^{1+2+3}$ .

Is it true that the product of any 10 consecutive positive integers must be divisible by $2^{1+2+3+4}$ ?

Yes, it is true No, it is not true

1 solution

Michael Mendrin
Nov 23, 2016

$1\times 2\times 3\times 4\times 5\times 6\times 7\times 8\times 9\times 10$ only has $8$ factors that are $2$

How about the maximum power of 2?

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