# How can I write the given argument into a logical proposition?

How can I write 'the number 100 can be written as the sum of 2 squares' into a logical proposition?

I'm starting with the basics of discrete mathematics and am not sure from what angle to approach it.

We've started learning about existential statements so I assume that would be the ideal approach? Not sure though - would appreciate a hand to approaching similar questions.

• Not sure if this is what you want but $\exists x, y$ such that $x^2 + y^2 = 100.$ You can further specify what ring you want the numbers from. – 伽罗瓦 Aug 8 '17 at 11:20

If you are talking about propositional logic, the answer is simple: $p$.
But I guess that you are talking about predicate logic. Then you have predicates and quantifiers. I'll use also standard symbols for certain predicates, such as $=$ and $\in\Bbb N$. The statement becomes $$\exists x(\exists y( x\in \Bbb N\wedge y\in \Bbb N \wedge x^2+y^2=100))$$