Is the following statement true or false?: There are integers $x$, $y$ and $z$ such that $15$ divides $2^x \cdot 3^y \cdot 7^z$

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score 7 · Answer 1 · answered Mar 08 '18 at 03:42

7

The statement is false. Consider the prime factorization of $15$ is $5 \cdot 3$, but we have $5 \cdot 3\cdot k=(2^x)(3^y)(7^z)$ The LHS has a factor of $5$, but the RHS does not. Therefore, since 5 is prime, we have that there are no solutions.

answered Mar 08 '18 at 03:42

user279540

71

Is the following statement true or false?: There are integers $x$, $y$ and $z$ such that $15$ divides $2^x \cdot 3^y \cdot 7^z$

1 Answers1