Is a number meeting these conditions divisible by forty-nine? I am not a mathematician, I'm a linguistics PhD student. As part of my research I need to put various convoluted sentences through various syntactic transformations and see then check whether people think they are true or not. Mathematical statements (well, some of them) suit my purposes very well, because they are less context dependent and can be straightforwardly assigned a truth value (i.e. be deemed true or false). The problem is that I'm not a mathematician. When these sentences get a bit convoluted, I have a bit of a problem knowing whether they are true or false myself (before they undergo various syntactic transformations). 
I have a particular sentence which states that if a given number is:


*

*an integer

*divisible by 7 (meaning it will yield an integer if divided by 7)

*a square number


then it is divisible by 49. I intuitively believe this to be correct (although I can't explain why). Is this actually true? I don't want to waste everybody's time by starting with an untrue untransformed sentence.

You can derive this fairly directly from Euclid's Lemma, which says that if a product $a \cdot b$ is divisible by prime $p$, then either $a$ or $b$ (or both) is divisible by $p$.
So, $n^2$ divisble by 7 means $n \cdot n$ divisible by 7 which (by Euclid's Lemma) means $n$ divisible by 7 and thus $n^2$ divisible by 49.
Of course it took even Euclid a little work to prove the Lemma
