True or False? There is an integer that's divisible by 13, can be written as...

[nikosan]

True or False?

There is an integer that is divisible by 13 and can be written as

(2 × 2 × · · · × 2) × (3 × 3 × · · · × 3) × (5 × 5 × · · · × 5).

is this asking to work out if a for 2^n, 3^2 and 5^n can all equal the same number divisible by 13? is that what the . . . means? If so, how do we work it out without doing it manually?

 

[Deleted member 4993]

True or False?

There is an integer that is divisible by 13 and can be written as

(2 × 2 × · · · × 2) × (3 × 3 × · · · × 3) × (5 × 5 × · · · × 5).

is this asking to work out if a for 2^n, 3^2 and 5^n can all equal the same number divisible by 13? is that what the . . . means? If so, how do we work it out without doing it manually?

Is that correct?

 

[nikosan]

Is that correct?

no, typo

 

[ksdhart]

Generally, when three ellipses appear in a math problem like that, it means that one or more items following the pattern have been omitted. In this case, the question is asking a true or false question: Does there exist a multiple of 13 that can be written as a multiplication of some number of 2s, 3s, and 5s (not necessarily the same number of each)? So, to answer this question, think about what you know about the factors of a number. Specifically, what does it mean for a number to be a multiple of 13?

 

[pka]

True or False?

There is an integer that is divisible by 13 and can be written as

(2 × 2 × · · · × 2) × (3 × 3 × · · · × 3) × (5 × 5 × · · · × 5).

is this asking to work out if a for 2^n, 3^2 and 5^n can all equal the same number divisible by 13? is that what the . . . means? If so, how do we work it out without doing it manually?

It means that if each of \(\displaystyle i,~j,~\&~,k\) is a non-negative integer then can \(\displaystyle 2^i\cdot 3^j\cdot 5^k\) have a factor of \(\displaystyle 13\)?

Look up prime factorization.

 

[Deleted member 4993]

True or False?

There is an integer that is divisible by 13 and can be written as

(2 × 2 × · · · × 2) × (3 × 3 × · · · × 3) × (5 × 5 × · · · × 5).

is this asking to work out if a for 2^n, 3^2 and 5^n can all equal the same number divisible by 13? is that what the . . . means? If so, how do we work it out without doing it manually?

Hint: 13 is a prime number