Writing a statement into symbolic logic

[cbarker1]

Dear Everyone,

I need to translate this following statement into a symbolic logical form of the statement:

The square of every odd integer is one more than an integral multiple of 4.

Thanks,

Cbarker1

 

[I like Serena]

Dear Everyone,

I need to translate this following statement into a symbolic logical form of the statement:

The square of every odd integer is one more than an integral multiple of 4.

Thanks,

Cbarker1

Something like:
$$\forall n \in \mathbb Z: n\text{ odd} \to n^2 \bmod 4 = 1$$
? (Wondering)

 

[Evgeny.Makarov]

The square of every odd integer is one more than an integral multiple of 4.

You can denote the whole statement by a single letter, say, $P$. This is to show that in order to make the problem meaningful, the problem author must specify the signature, or vocabulary: constants, functional symbols and predicate symbols that can be used in the formula. Ideally the author should also specify the interpretation of that signature because this statement is written differently over natural numbers and over reals.

But, guessing the author's intent, the answer is probably
\[
\forall m\exists n\,(2m+1)(2m+1)=4n+1.
\]